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Popular >

derivative of x^2(6-x^3)

Solution

\frac{d}{d x} (x^{2} (6 - x)^{3})

Solution

2 x (6 - x)^{3} - 3 x^{2} (6 - x)^{2}

Solution steps

\frac{d}{d x} (x^{2} (6 - x)^{3})

Apply the Product Rule:

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

f = x^{2}, g = (6 - x)^{3}

= \frac{d}{d x} (x^{2}) (6 - x)^{3} + \frac{d}{d x} ((6 - x)^{3}) x^{2}

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

\frac{d}{d x} ((6 - x)^{3}) = - 3 (6 - x)^{2}

= 2 x (6 - x)^{3} + (- 3 (6 - x)^{2}) x^{2}

Simplify

= 2 x (6 - x)^{3} - 3 x^{2} (6 - x)^{2}

Popular Examples

integral of 1/(x^2+8x+20)

\int \frac{1}{x ^{2} + 8 x + 20} d x

limit as x approaches 0 of 4/x-4/(|x|)

x \to 0 lim (\frac{4}{x} - \frac{4}{∣ x ∣})

y^{^{'}} + y = 5 sin (2 x)

(\partial)/(\partial x)(sin(nx)e^{-n^2t})

\frac{\partial}{\partial x} (sin (n x) e^{- n^{2} t})

limit as x approaches infinity of 1-e^x

x \to \infty lim (1 - e^{x})

Frequently Asked Questions (FAQ)

What is the derivative of x^2(6-x^3) ?
The derivative of x^2(6-x^3) is 2x(6-x)^3-3x^2(6-x)^2
What is the first derivative of x^2(6-x^3) ?
The first derivative of x^2(6-x^3) is 2x(6-x)^3-3x^2(6-x)^2