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Popular >

derivative of f(x)=(x-4)(x^2+8)

Solution

derivative of

f (x) = (x - 4) (x^{2} + 8)

Solution

3 x^{2} - 8 x + 8

Solution steps

\frac{d}{d x} ((x - 4) (x^{2} + 8))

Apply the Product Rule:

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

f = x - 4, g = x^{2} + 8

= \frac{d}{d x} (x - 4) (x^{2} + 8) + \frac{d}{d x} (x^{2} + 8) (x - 4)

\frac{d}{d x} (x - 4) = 1

\frac{d}{d x} (x^{2} + 8) = 2 x

= 1 \cdot (x^{2} + 8) + 2 x (x - 4)

Simplify

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

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

Popular Examples

y^{^{'}} = 4 y + y^{4}

derivative of (x^2-9x+14/((x-5)(x-10)))

\frac{d}{d x} (\frac{x ^{2} - 9 x + 14}{( x - 5 ) ( x - 10 )})

(\partial)/(\partial x)(yx^{-1})

\frac{\partial}{\partial x} (y x^{- 1})

((x^2+1)dy)/(dx)+6x(y-1)=0,y(0)=6

\frac{( x ^{2} + 1 ) d y}{d x} + 6 x (y - 1) = 0, y (0) = 6

integral of 1/(x^3)ln(x)

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

Frequently Asked Questions (FAQ)

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