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Popular >

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

Solution

derivative of

(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

y^'+y/(2x)= x/(y^3)

y^{^{'}} + \frac{y}{2 x} = \frac{x}{y ^{3}}

tangent of f(x)=(3x)/((x+1)^2),(0,0)tangent of

f (x) = \frac{3 x}{( x + 1 ) ^{2}}, (0, 0)

derivative of (3x^2+19x-7(14x^3+12x))

\frac{d}{d x} ((3 x^{2} + 19 x - 7) (14 x^{3} + 12 x))

limit as x approaches 0 of 1/(x-2)

x \to 0 lim (\frac{1}{x - 2})

x^2y^'-xy-x^3sin(x)=0

x^{2} y^{^{'}} - x y - x^{3} sin (x) = 0

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)