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Popular >

derivative of x^3(x-5^2)

Solution

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

Solution

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}

Popular Examples

5 y y^{^{'}} = x

limit as h approaches infinity of (5h^4-2h^2+3)/(3h^3+2h^2+h)

h \to \infty lim (\frac{5 h ^{4} - 2 h ^{2} + 3}{3 h ^{3} + 2 h ^{2} + h})

integral of (x^2+y^2)^{(-3/2)}

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

(dy)/(dx)=2x(1+y)e^{x^2}

\frac{d y}{d x} = 2 x (1 + y) e^{x^{2}}

derivative of y=2x^2+1 derivative of

y = 2 x^{2} + 1

Frequently Asked Questions (FAQ)

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