Differentiation help please!?

Question

Differentiate the following functions of x (using either the product, quotient or chain rule)

f(x) = (x-5)(4x²+1)^5

f(x) = 2x²/(x-1)³

f(x) = lnx/√x

Thanks very much, in advance :)

Answer 1

Let us look at the first problem. We will need the product rule and chain rule in that order.

f(x) = (x-5)(4x²+1)^5

f'(x) = (x-5)*5(4x²+1)^4*8x + (4x²+1)^5*1

I will leave simplifying to you.

The second we can use the quotient rule or if expressed with negative exponents the product rule again.

f(x) = 2x²/(x-1)³

I will leave that to you.

f(x) = lnx/√x

f'(x) = [√x*1/x - ln x*1/2*1/√x]/x

I leave simplification to yo.