What is the derivative of x^3(x-5)^2 ?

The derivative of x^3(x-5)^2 is 5x^4-40x^3+75x^2

What is the first derivative of x^3(x-5)^2 ?

The first derivative of x^3(x-5)^2 is 5x^4-40x^3+75x^2

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derivative of

x^{3} (x - 5)^{2}

5 x^{4} - 40 x^{3} + 75 x^{2}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = (x - 5)^{2}

= \frac{d}{d x} (x^{3}) (x - 5)^{2} + \frac{d}{d x} ((x - 5)^{2}) x^{3}

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

\frac{d}{d x} ((x - 5)^{2}) = 2 (x - 5)

= 3 x^{2} (x - 5)^{2} + 2 (x - 5) x^{3}

Simplify

3 x^{2} (x - 5)^{2} + 2 (x - 5) x^{3} : 5 x^{4} - 40 x^{3} + 75 x^{2}

= 5 x^{4} - 40 x^{3} + 75 x^{2}

0.05 \cdot x \cdot ln (\frac{10}{x}), x = 1

\frac{5 s}{s ^{2} + 2 s + 5}

\int 3 cos^{2} (x) sin^{2} (x) d x

x \to 0 lim (x^{3 x})

\int_{1}^{2} \frac{4 + u ^{2}}{u ^{3}} d u

What is the derivative of x^3(x-5)^2 ?
The derivative of x^3(x-5)^2 is 5x^4-40x^3+75x^2
What is the first derivative of x^3(x-5)^2 ?
The first derivative of x^3(x-5)^2 is 5x^4-40x^3+75x^2