Question

How do you find the derivative of `Y= ( x^3 + 5x^2 - 3 )( x^2 - 1 )^5`?

Answer 1

Refer explanation section

Explanation:

Y=`(x^3+5x^2−3)(x^2−1)^5`
`dy/dx`= `(x^3+5x^2−3)(5)(x^2 - 1)^4(2x)+(x^2−1)^5(3x^2 + 10x)`
`dy/dx`= `(x^3+5x^2−3)(10x)(x^2 - 1)^4+(x^2−1)^5(3x^2 + 10x)`
`dy/dx`= `(10x^4+50x^3−30x)(x^2 - 1)^4+(x^2−1)^5(3x^2 + 10x)`