What is the derivative of f(x)=2(x^3-x)^4 ?

The derivative of f(x)=2(x^3-x)^4 is 8(x^3-x)^3(3x^2-1)

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

The first derivative of f(x)=2(x^3-x)^4 is 8(x^3-x)^3(3x^2-1)

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derivative of

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

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

Solution steps

\frac{d}{d x} (2 (x^{3} - x)^{4})

Take the constant out:

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

= 2 \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

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

Simplify

= 8 (x^{3} - x)^{3} (3 x^{2} - 1)

\frac{\partial}{\partial y} (sin^{2} (x y))

y^{^{'}} + \frac{4 y}{x} = - \frac{3}{x}, y (1) = - 2

\int - 2 cos (\frac{x}{2}) d x

x \to 2 lim (x^{2} + 3 x)

\int 9 x^{- 2} d x

What is the derivative of f(x)=2(x^3-x)^4 ?
The derivative of f(x)=2(x^3-x)^4 is 8(x^3-x)^3(3x^2-1)
What is the first derivative of f(x)=2(x^3-x)^4 ?
The first derivative of f(x)=2(x^3-x)^4 is 8(x^3-x)^3(3x^2-1)