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Popular >

derivative of x^3(x-7)^2

Solution

derivative of

x^{3} (x - 7)^{2}

Solution

5 x^{4} - 56 x^{3} + 147 x^{2}

Solution steps

\frac{d}{d x} (x^{3} (x - 7)^{2})

Apply the Product Rule:

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

f = x^{3}, g = (x - 7)^{2}

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

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

\frac{d}{d x} ((x - 7)^{2}) = 2 (x - 7)

= 3 x^{2} (x - 7)^{2} + 2 (x - 7) x^{3}

Simplify

3 x^{2} (x - 7)^{2} + 2 (x - 7) x^{3} : 5 x^{4} - 56 x^{3} + 147 x^{2}

= 5 x^{4} - 56 x^{3} + 147 x^{2}

Popular Examples

tangent of y=x^2+3 tangent of

y = x^{2} + 3

(\partial)/(\partial y)(sqrt(41-x^2-4y^2))

\frac{\partial}{\partial y} (41 - x^{2} - 4 y^{2})

y^{^{''}} + \frac{y}{a} = 0

integral of 1/(x^3+x^2+x+1)

\int \frac{1}{x ^{3} + x ^{2} + x + 1} d x

integral from 0 to 1 of pi(x^2-x^4)

\int_{0}^{1} π (x^{2} - x^{4}) d x

Frequently Asked Questions (FAQ)

What is the derivative of x^3(x-7)^2 ?
The derivative of x^3(x-7)^2 is 5x^4-56x^3+147x^2
What is the first derivative of x^3(x-7)^2 ?
The first derivative of x^3(x-7)^2 is 5x^4-56x^3+147x^2