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Popular >

derivative of x^3(x-1)^2

Solution

derivative of

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

Solution

5 x^{4} - 8 x^{3} + 3 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 x^{2} (x - 1)^{2} + 2 (x - 1) x^{3} : 5 x^{4} - 8 x^{3} + 3 x^{2}

= 5 x^{4} - 8 x^{3} + 3 x^{2}

Popular Examples

integral of (x+1)/((x-1)^3)

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

integral of (tan(x))/1

\int \frac{tan ( x )}{1} d x

y^{^{'}} = t - 2 y

integral from 2 to infinity of 1/(x^4)

\int_{2}^{\infty} \frac{1}{x ^{4}} d x

tangent of f(x)=x^2-7x+12,\at x=2 tangent of

f (x) = x^{2} - 7 x + 12, at x = 2

Frequently Asked Questions (FAQ)

What is the derivative of x^3(x-1)^2 ?
The derivative of x^3(x-1)^2 is 5x^4-8x^3+3x^2
What is the first derivative of x^3(x-1)^2 ?
The first derivative of x^3(x-1)^2 is 5x^4-8x^3+3x^2