What is the derivative of 5(x^3-x)^4 ?

The derivative of 5(x^3-x)^4 is 20(x^3-x)^3(3x^2-1)

What is the first derivative of 5(x^3-x)^4 ?

The first derivative of 5(x^3-x)^4 is 20(x^3-x)^3(3x^2-1)

derivative of

5 (x^{3} - x)^{4}

20 (x^{3} - x)^{3} (3 x^{2} - 1)

Solution steps

\frac{d}{d x} (5 (x^{3} - x)^{4})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} ((x^{3} - x)^{4})

Apply the chain rule:

4 (x^{3} - x)^{3} \frac{d}{d x} (x^{3} - x)

= 4 (x^{3} - x)^{3} \frac{d}{d x} (x^{3} - x)

\frac{d}{d x} (x^{3} - x) = 3 x^{2} - 1

= 5 \cdot 4 (x^{3} - x)^{3} (3 x^{2} - 1)

Simplify

= 20 (x^{3} - x)^{3} (3 x^{2} - 1)

\int x (2 sec^{2} (x) + tan^{2} (x)) d x

\frac{d}{d y} (4 - y^{2})

\int_{- 7}^{0} (4 + 49 - x^{2}) d x

\int \frac{2 x ^{2} + 5 x + 2}{( x ^{2} + 1 ) ^{2}} d x

\int \frac{25 - 16 x ^{2}}{x} d x

What is the derivative of 5(x^3-x)^4 ?
The derivative of 5(x^3-x)^4 is 20(x^3-x)^3(3x^2-1)
What is the first derivative of 5(x^3-x)^4 ?
The first derivative of 5(x^3-x)^4 is 20(x^3-x)^3(3x^2-1)