MathsNet: D - Differentiation - Finding tangents 1

Online Mathematics

Universal (all site questions)

Log On

Forgotten Password?

Module

33-D Geometry, 3D Shapes

AAlgebra, Algebra and Functions, Algorithms, Algorithms on graphs, Applications, Applications of the integrals, Area, Areas, Areas Related to Circles, Arithmetic, Arithmetic Progressions, Algebraic Expressions, Applying Congruence and Similarity, Approximate Solutions Using Graph

BBinomial Theorem, The Binomial Distribution, The Normal Distribution, Probability

CCalculus, Centres of Mass, Circles, Collecting data, Collisions, Combinations of random variables, Complex Numbers, Complex Numbers and Quadratic Equations, Compound measures, Construction, Constructions, Continuous Distributions, Continuous Random Variables, Coordinate geometry, Coordinates, Correlation and Regression, Critical path analysis, Summary

DDecimals, Determinants, Differential equations, Differentiation, Dimensions, Direct and indirect proportion, Discrete Random Variables, Displaying data, Drawing, Dynamics, Statics, Calculus

EEnlargement, Equivalence classes, Estimation, Exam preparation, Exponentials and logs, Differentiation, Dynamics

F1st Order Differential Equations, Financial mathematics, Flows in a network, Fourier series, Fractions, Functions, Functions and expressions, Further Dynamics, Summary

GGeometry, Goodness of fit, Graphic calculators, Graphics calculator, Graphs, Groups, Summary

HHyperbolic Functions, Hypothesis Tests, Hypothesis Testing

IImpulse and momentum in 2D, Indices, Inequalities, Integer Arithmetic, Integration, Introduction to 3-Dimesional Geometry, Inverse Laplace transforms, Inverse Trigonometric Functions, Irrational Functions, Inequalities in One Variable

KKinematics, Summary

LLaplace transforms, Limits and continuity, Limits and Derivatives, Linear Equations in 2 Variables, Linear programming, Linear-Programming, Summary

MMaclaurin and Taylor Series, Matchings, Mathematical modelling, Matrices, Matrix algebra, Measures, Mensuration, Moments, Motion in a circle, Multivariable calculus, Summary

NNotation, Number, Number and algebra, Numerical Methods, The Normal Distribution

OOscillations, Summary

PPaper 1, Paper 2, Percentages, Perimeter area volume, Permutation and Combinations, Piecewise functions, Polar Coordinates, Polynomials, Powers and roots, Probability, Proof, Properties of shapes, The Poisson Distribution, Statistics

QQuadratic equations, Quadratic functions

RRoute inspection, Summary

S2nd Order Differential Equations, Sampling, Scales and ratios, Sequence and Series, Sequences, Sequences and series, Sets, Shape and space, Simple equations, Simulation, Simultaneous equations, Statics, Statistical models, Statistics, Summarising data, Surds, Surface Area and Volume, Surface Areas and Volumes, Symbolic Logic, Symbols, Systems of D.E.s, Systems of Rigid Bodies, Straight Line Graphs, Sketching Graphs of Functions, Solving Quadratics by Factorising, Simultaneous Linear Equations, Special Sequences

TTransformations, Travelling salesman problem, Triangles, Trigonometry

UUpper and lower bounds, Using a calculator

VVectors

WWork and Energy

MAPSelect Using the Interactive Map

Awarding Bodies

Page ID: 89

D | Differentiation | Curves | «Finding tangents 1»

tangent and normal

To find the gradient of a tangent to a curve y=f(x) at a given point x=a:
firstly differentiate the equation of the curve in order to find \displaystyle\frac{dy}{dx} ,
secondly substitute into this expression the value x=a.

Change

Steps

All

Change

Steps

All

O

O

O

O

+

r

-

≡

☰

Summary/Background

If y = ax^n then \displaystyle\frac{dy}{dx} = anx^{n-1} and if y = a then \displaystyle \frac{dy}{dx} = 0, where a is a constant.
These work for all values of n, positive or negative, decimal or fraction.

Software/Applets used on this page

jsMath

This page uses jsMath
You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

This question appears in the following syllabi:

Syllabus	Module	Section	Topic	Exam Year
AP Calculus AB (USA)	3	Differentiation	Curves	-
AP Calculus BC (USA)	3	Differentiation	Curves	-
AQA A-Level (UK - Pre-2017)	C1	Differentiation	Curves	-
AQA AS Maths 2017	Pure Maths	Differentiation	Tangents and Normals	-
AQA AS/A2 Maths 2017	Pure Maths	Differentiation	Tangents and Normals	-
CBSE XII (India)	Calculus	Applications of Derivatives	Tangents and normals	-
CCEA A-Level (NI)	C1	Differentiation	Curves	-
CIE A-Level (UK)	P1	Differentiation	Curves	-
Edexcel A-Level (UK - Pre-2017)	C1	Differentiation	Curves	-
Edexcel AS Maths 2017	Pure Maths	Differentiation	Tangents and Normals	-
Edexcel AS/A2 Maths 2017	Pure Maths	Differentiation	Tangents and Normals	-
I.B. Higher Level	6	Differentiation	Curves	-
I.B. Standard Level	6	Differentiation	Curves	-
Methods (UK)	M8	Differentiation	Curves	-
I.B. (MSSL)	7	Differentiation	Curves	-
OCR A-Level (UK - Pre-2017)	C1	Differentiation	Curves	-
OCR AS Maths 2017	Pure Maths	Applying Differentiation	Tangents and Normals	-
OCR MEI AS Maths 2017	Pure Maths	Applying Differentiation	Tangents and Normals	-
OCR-MEI A-Level (UK - Pre-2017)	C2	Differentiation	Curves	-
Pre-U A-Level (UK)	4	Differentiation	Curves	-
Scottish (Highers + Advanced)	HM1	Differentiation	Curves	-
Scottish Highers	M1	Differentiation	Curves	-
Universal (all site questions)	D	Differentiation	Curves	-
WJEC A-Level (Wales)	C1	Differentiation	Curves	-