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Popular >

derivative of x(x^4+8^3)

Solution

\frac{d}{d x} (x (x^{4} + 8)^{3})

Solution

(x^{4} + 8)^{3} + 12 x^{4} (x^{4} + 8)^{2}

Solution steps

\frac{d}{d x} (x (x^{4} + 8)^{3})

Apply the Product Rule:

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

f = x, g = (x^{4} + 8)^{3}

= \frac{d x}{d x} (x^{4} + 8)^{3} + \frac{d}{d x} ((x^{4} + 8)^{3}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{4} + 8)^{3}) = 12 x^{3} (x^{4} + 8)^{2}

= 1 \cdot (x^{4} + 8)^{3} + 12 x^{3} (x^{4} + 8)^{2} x

Simplify

1 \cdot (x^{4} + 8)^{3} + 12 x^{3} (x^{4} + 8)^{2} x : (x^{4} + 8)^{3} + 12 x^{4} (x^{4} + 8)^{2}

= (x^{4} + 8)^{3} + 12 x^{4} (x^{4} + 8)^{2}

Popular Examples

limit as x approaches-3 of ln(x^4-3x+10)

x \to - 3 lim (ln (x^{4} - 3 x + 10))

integral of (2x+5)/(3x(x+3)^2)

\int \frac{2 x + 5}{3 x ( x + 3 ) ^{2}} d x

(\partial)/(\partial y)(xy+8/x+8/y)

\frac{\partial}{\partial y} (x y + \frac{8}{x} + \frac{8}{y})

derivative of sqrt(7-2x)

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

limit as x approaches 0 of xcot(7/11 x)

x \to 0 lim (x cot (\frac{7}{11} x))

Frequently Asked Questions (FAQ)

What is the derivative of x(x^4+8^3) ?
The derivative of x(x^4+8^3) is (x^4+8)^3+12x^4(x^4+8)^2
What is the first derivative of x(x^4+8^3) ?
The first derivative of x(x^4+8^3) is (x^4+8)^3+12x^4(x^4+8)^2