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)

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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)

x \to 0 + lim (x ln (tan (2 x)))

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

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 4

x \to \frac{π}{4} lim (\frac{sin ( x )}{x})

\frac{d y}{d t} = 2 y

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)