What is the derivative of 7(x^3-x^4) ?

The derivative of 7(x^3-x^4) is 28(x^3-x)^3(3x^2-1)

What is the first derivative of 7(x^3-x^4) ?

The first derivative of 7(x^3-x^4) is 28(x^3-x)^3(3x^2-1)

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\frac{d}{d x} (7 (x^{3} - x)^{4})

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

Solution steps

\frac{d}{d x} (7 (x^{3} - x)^{4})

Take the constant out:

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

= 7 \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

= 7 \cdot 4 (x^{3} - x)^{3} (3 x^{2} - 1)

Simplify

= 28 (x^{3} - x)^{3} (3 x^{2} - 1)

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

\frac{d}{d x} (6 x + 29 cos (\frac{3 x}{4}) + 5 x^{2} + 3)

\int (2 x - 3)^{5} d x

y \to x lim (\frac{y ^{\frac{2}{3}} - x ^{\frac{2}{3}}}{y - x})

f (x) = x^{2}, at x = 5

What is the derivative of 7(x^3-x^4) ?
The derivative of 7(x^3-x^4) is 28(x^3-x)^3(3x^2-1)
What is the first derivative of 7(x^3-x^4) ?
The first derivative of 7(x^3-x^4) is 28(x^3-x)^3(3x^2-1)