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Popular >

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

Solution

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

Solution

(x^{2} + 2)^{3} + 6 x (x^{2} + 2)^{2} (x - 1)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot (x^{2} + 2)^{3} + 6 x (x^{2} + 2)^{2} (x - 1)

Simplify

= (x^{2} + 2)^{3} + 6 x (x^{2} + 2)^{2} (x - 1)

Popular Examples

(\partial)/(\partial x)(ln(2+x^2y^2))

\frac{\partial}{\partial x} (ln (2 + x^{2} y^{2}))

integral of (6x^3)/(sqrt(x^2+9))

\int \frac{6 x ^{3}}{x ^{2} + 9} d x

limit as t approaches-1 of t^2-1

t \to - 1 lim (t^{2} - 1)

integral of sin(5x)*cos(2x)

\int sin (5 x) \cdot cos (2 x) d x

derivative of f(t)=ln(t^9+5)derivative of

f (t) = ln (t^{9} + 5)

Frequently Asked Questions (FAQ)

What is the derivative of (x-1(x^2+2)^3) ?
The derivative of (x-1(x^2+2)^3) is (x^2+2)^3+6x(x^2+2)^2(x-1)
What is the first derivative of (x-1(x^2+2)^3) ?
The first derivative of (x-1(x^2+2)^3) is (x^2+2)^3+6x(x^2+2)^2(x-1)