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What is the chain rule?

Up until now you may have been given functions like f(x)= 7x^3 +cos(x) and been told just to differentiate. What your teacher really meant was to differentiate with respect to x. The chain rule allows us to ...
JM
Answered by James M. • Maths tutor
3821 Views

Find the integral of 4sqrt(x) - 6/x^3.

The easiest way to do this is to break the integral up into it's separate parts. We have:integral of 4sqrt(x)andintegral of -6/x^3 Both of which have constants that can be taken out, i.e. 4 and 6, respective...
SP
Answered by Sam P. • Maths tutor
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Give the first and second derivative of the function f(x) = 5/x - 9x + 4

Re-write f(x) as f(x) = 5x^(-1) - 9x + 42) Find first derivative as usual - multiply each term by it's power and subtract 1 from the power:f'(x) = (-1)(5x^(-2)) - (1)(9)Simplify to get f'(x) = -5/x^(2) - 9Fi...
HB
Answered by Harvey B. • Maths tutor
3544 Views

Solve the simultaneous equations: 5x + y = 21 and x - 3y = 9

x = 4.5y = -1.5To answer this question, first, rearrange the first equation to make y the subject: 5x + y = 21 --> y = 21 - 5xYou can now substitute this value of y into the second equation: x - 3(21 - 5x...
SA
Answered by Sophie A. • Maths tutor
4294 Views

How do you solve integrals which are the result of a chain rule e.g. the integral of sin(2x+1)

∫sin(2x + 1)dx[newline]In this case the easiest way to solve the integral is to perform a substitution. The substitution should reduce the integral to something you can solve. In this case we will[newline]le...
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Answered by Sean N. • Maths tutor
1773 Views