What is the derivative of (3x-2)^3(x^3+1)^2 ?

The derivative of (3x-2)^3(x^3+1)^2 is 9(3x-2)^2(x^3+1)^2+6x^2(x^3+1)(3x-2)^3

What is the first derivative of (3x-2)^3(x^3+1)^2 ?

The first derivative of (3x-2)^3(x^3+1)^2 is 9(3x-2)^2(x^3+1)^2+6x^2(x^3+1)(3x-2)^3

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derivative of

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

9 (3 x - 2)^{2} (x^{3} + 1)^{2} + 6 x^{2} (x^{3} + 1) (3 x - 2)^{3}

Solution steps

\frac{d}{d x} ((3 x - 2)^{3} (x^{3} + 1)^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (3 x - 2)^{3}, g = (x^{3} + 1)^{2}

= \frac{d}{d x} ((3 x - 2)^{3}) (x^{3} + 1)^{2} + \frac{d}{d x} ((x^{3} + 1)^{2}) (3 x - 2)^{3}

\frac{d}{d x} ((3 x - 2)^{3}) = 9 (3 x - 2)^{2}

\frac{d}{d x} ((x^{3} + 1)^{2}) = 6 x^{2} (x^{3} + 1)

= 9 (3 x - 2)^{2} (x^{3} + 1)^{2} + 6 x^{2} (x^{3} + 1) (3 x - 2)^{3}

\int x^{3} x^{2} + 12 d x

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

4 x - x^{2}, 0, 2

x^{2} - 4, - 2, 2

f (x) = (7 x^{3} + x^{2})^{\frac{2}{3}}

What is the derivative of (3x-2)^3(x^3+1)^2 ?
The derivative of (3x-2)^3(x^3+1)^2 is 9(3x-2)^2(x^3+1)^2+6x^2(x^3+1)(3x-2)^3
What is the first derivative of (3x-2)^3(x^3+1)^2 ?
The first derivative of (3x-2)^3(x^3+1)^2 is 9(3x-2)^2(x^3+1)^2+6x^2(x^3+1)(3x-2)^3