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

The derivative of f(x)=x^3(x-8)^2 is 5x^4-64x^3+192x^2

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

The first derivative of f(x)=x^3(x-8)^2 is 5x^4-64x^3+192x^2

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derivative of

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

5 x^{4} - 64 x^{3} + 192 x^{2}

Solution steps

\frac{d}{d x} (x^{3} (x - 8)^{2})

Apply the Product Rule:

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

f = x^{3}, g = (x - 8)^{2}

= \frac{d}{d x} (x^{3}) (x - 8)^{2} + \frac{d}{d x} ((x - 8)^{2}) x^{3}

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

\frac{d}{d x} ((x - 8)^{2}) = 2 (x - 8)

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

Simplify

3 x^{2} (x - 8)^{2} + 2 (x - 8) x^{3} : 5 x^{4} - 64 x^{3} + 192 x^{2}

= 5 x^{4} - 64 x^{3} + 192 x^{2}

\frac{d y}{d x} = e^{2 y} sin (3 x)

f (x) = \frac{7}{x}, at x = 1

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

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

x^{2} - 6 x, 0

What is the derivative of f(x)=x^3(x-8)^2 ?
The derivative of f(x)=x^3(x-8)^2 is 5x^4-64x^3+192x^2
What is the first derivative of f(x)=x^3(x-8)^2 ?
The first derivative of f(x)=x^3(x-8)^2 is 5x^4-64x^3+192x^2