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

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

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

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

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derivative of

f (x) = 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)

\frac{d}{d x} (\frac{( x - 2 )}{x - 1})

h (x) = (x + 1)^{7} - 7 x - 3

\int e^{x} cos (7 x) d x

2 x, x, 2

\frac{\partial}{\partial y} (cos (2 y) - 3 x^{2} y^{2})

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