Thread: Chain Rule Derivative

Find the Derivative using the Chain Rule:

x^3(2x-5)^4

Originally Posted by Luckyjoshua

Find the Derivative using the Chain Rule:

x^3(2x-5)^4

You also need to use product rule.
The two functions here are,
x^3
(2x-4)^4

The respective derivatives are:
3x^2----> Power rule
2*4(2x-4)^3=8(2x-4)^3---->Chain Rule

Now apply the product rule,
u'v+uv'
We have,
[3x^2][(2x-4)^4]+[x^3][8(2x-4)^3]
Thus,
3x^2(2x-4)^4+8x^3(2x-4)^3
Factor,
x^2(2x-4)^3[3(2x-4)+8x(2x-4)]
Open,
x^2(2x-4)^3[6x-4+16x^2-32x]
Thus,
x^2(2x-4)^3[16x^2-26x-4]
Factor,
2x^2(2x-4)^3(8x^2-13x-2)