Question

Find the Derivative of (7x^2-6)^8(-4x^2-3)^9

Answer 1

This is a case of the differentiation of a product, for which the rule is

d(u.v)/dx = u.dv/dx+v.du
For example, the derivative of xsin(x) can be found as:
d(xsin(x))/dx
=xcos(x)+1.sin(x)
=xcos(x)+sin(x)

Also, the differentiation of the powers of a binomial can take advantage of the chain rule:
d(x²+1)³/dx
=3(x²+1)².2x
=6x(x²+1)²

Based on these two rules, you should have no problem working out the answer.
Post your answer for a check if you wish.

Note: When you add up terms and factorize correctly, you should see the following as a factor:
(119*x^2-12)...