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Differentiate y = (x^2 + 3)^2

We have to use the chain rule here. If we set u to the inside of the bracket, u = x^2 + 3 and differentiating we get du/dx = 2x. Now the original expression becomes y = u^2. Differentiating this with respect...
MH
Answered by Matthew H. • Maths tutor
8316 Views

How to differentiate tan(x)?

tanx = sinx/cosx. Express this as: sinx*(cosx)^-1. Remembering the product rule: "y = f(x)g(x), dy/dx = f'(x)g(x) + f(x)g'(x)". sinx differentiates to cosx and cosx differentiates to -sinx. Also, r...
KA
Answered by Kai A. • Maths tutor
12851 Views

How to complete the square?

This is a handy trick for quadratic equations ax^2 + bx + c = 0. e.g. (x^2 + 5x + 6). So a = 1, b = 5 and c = 6. To complete the square, let x^2 + 5x + 6 = 0. Then, take 6 to the other side to get x^2 + 5x =...
JP
Answered by Jigar P. • Maths tutor
5135 Views

Differentiate y=sin(x)/5x^3 with respect to x

In order to complete this question we need to use the quotient rule (i.e. if an equation is of the form h(x)=f(x)/g(x) then h'(x)=(g(x) f'(x)-g'(x) f(x))/g(x)^2).In our example f'(x)=cos(x),g'(x)=15x^2, ther...
KZ
Answered by Kirill Z. • Maths tutor
4460 Views

Find the stationary points of the function y = (1/3)x^3 + (1/2)x^2 - 6x + 15

A stationary point is a point on the function where the gradient is zero. The phrase 'stationary point' coming up in a question always indicates that differentiation may be useful to solve it. In this case, ...
MH
Answered by Matthew H. • Maths tutor
10137 Views