Question

Differentiate F(x) = (x^4 + 3x^2 - 2)^5

Answer 1

We have
\[f(x)= (x^4+3x^2-2)^5\]
Let's differentiate this with respect to x
\[f'(x)=\frac{d}{dx}( x^4+3x^2-2)^5\]
we get now
\[f'(x)= 5(x^4+3x^2-2)^{(5-1)} \times \frac{d}{dx}(x^4+3x^2-2)\]
we get
\[f'(x)= 5(x^4+3x^2-2)^4 \times(4x^3+6x)\]