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Popular Calculus >

derivative of 1/(x^7+1/(x^8))

Solution

\frac{d}{d x} (\frac{1}{x ^{7}} + \frac{1}{x ^{8}})

Solution

- \frac{7}{x ^{8}} - \frac{8}{x ^{9}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{7}} + \frac{1}{x ^{8}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{x ^{7}}) + \frac{d}{d x} (\frac{1}{x ^{8}})

\frac{d}{d x} (\frac{1}{x ^{7}}) = - \frac{7}{x ^{8}}

\frac{d}{d x} (\frac{1}{x ^{8}}) = - \frac{8}{x ^{9}}

= - \frac{7}{x ^{8}} - \frac{8}{x ^{9}}

Graph

Popular Examples

sum from n=1 to infinity of ne^{7n}

n = 1 \sum \infty n e^{7 n}

derivative of x/((1+x^2))

d er i v a t i v e \frac{x}{( 1 + x ^{2} )}

limit as x approaches-4 of (x^2+2)/(x+5)

x \to - 4 lim (\frac{x ^{2} + 2}{x + 5})

\frac{d y}{d x} = x y^{2}

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

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

Frequently Asked Questions (FAQ)

What is the derivative of 1/(x^7+1/(x^8)) ?
The derivative of 1/(x^7+1/(x^8)) is -7/(x^8)-8/(x^9)
What is the first derivative of 1/(x^7+1/(x^8)) ?
The first derivative of 1/(x^7+1/(x^8)) is -7/(x^8)-8/(x^9)