What is the derivative of 9(x^3-x^4) ?

The derivative of 9(x^3-x^4) is 36(x^3-x)^3(3x^2-1)

What is the first derivative of 9(x^3-x^4) ?

The first derivative of 9(x^3-x^4) is 36(x^3-x)^3(3x^2-1)

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\frac{d}{d x} (9 (x^{3} - x)^{4})

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

Solution steps

\frac{d}{d x} (9 (x^{3} - x)^{4})

Take the constant out:

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

= 9 \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

= 9 \cdot 4 (x^{3} - x)^{3} (3 x^{2} - 1)

Simplify

= 36 (x^{3} - x)^{3} (3 x^{2} - 1)

\int \frac{x}{( x ^{2} + a ^{2} ) ^{\frac{3}{2}}} d x

y^{^{''}} - 6 y^{^{'}} + 12 y = sin (2 x)

y^{^{''}} + y = e^{- x}

y = x (49.7)

\int \frac{1}{e ^{- 2 x}} d x

What is the derivative of 9(x^3-x^4) ?
The derivative of 9(x^3-x^4) is 36(x^3-x)^3(3x^2-1)
What is the first derivative of 9(x^3-x^4) ?
The first derivative of 9(x^3-x^4) is 36(x^3-x)^3(3x^2-1)