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Find the derivative of the function y=3x^2e^(2x)sin(x).

y is the product of three different function, so we would use the product rule in order to calculate the derivative of the curve. In order to apply the product rule we need to find the derivatives of each of...
SR
Answered by Shreya R. • Maths tutor
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f(x)=(2x+1)/(x-1) with domain x>3. (a)Find the inverse of f(x). (b)Find the range of f(x). (c) g(x)=x+5 for all x. Find the value of x such that fg(x)=3.

(a) Let y=f(x). Then y = (2x+1)/(x-1). Rearrange the equation to get x in terms of y to obtain the inverse function. This gives x=(1+y)/(y-2). So the inverse of f is f -1 (x)=(1+x)/(x-2) (b) Drawing a graph ...
LA
Answered by Lutfha A. • Maths tutor
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Find dy/dx for y = x^3*e^x*cos(x)

In this problem, we see that y is a product of 3 functions of x. That means that in order to find dy/dx we need to use the product rule. The product rule tells us that in this case we should differentiate on...
LN
Answered by Lyudmil N. • Maths tutor
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Solve x² ≥ | 5x - 6 | (Question from AQA Core 3 June 2016)

To solve this question we can break it down in to a multiple small stages. The first thing to tackle is the use of modulus around 5x - 6. This effectively means we have two equations to solve: EQ1: x² ≥ 5x -...
JH
Answered by James H. • Maths tutor
7418 Views

Use chain rule and implicit differentiation to find dy/dx for y^3 = 1 + 3*x^2, then show that they are equal

When using the Chain Rule, it is best to put our equal in a form where there are no operations performed on the subject. i.e. y = (1 + 3*x 2 ) 1/3 Then to help make it clear what we need to do, state the rul...
JP
Answered by Joshua P. • Maths tutor
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