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Popular >

derivative of-7csc(x+1/(x^5))

Solution

\frac{d}{d x} (- 7 csc (x) + \frac{1}{x ^{5}})

Solution

7 cot (x) csc (x) - \frac{5}{x ^{6}}

Solution steps

\frac{d}{d x} (- 7 csc (x) + \frac{1}{x ^{5}})

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (7 csc (x)) + \frac{d}{d x} (\frac{1}{x ^{5}})

\frac{d}{d x} (7 csc (x)) = - 7 cot (x) csc (x)

\frac{d}{d x} (\frac{1}{x ^{5}}) = - \frac{5}{x ^{6}}

= - (- 7 cot (x) csc (x)) - \frac{5}{x ^{6}}

Simplify

= 7 cot (x) csc (x) - \frac{5}{x ^{6}}

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Frequently Asked Questions (FAQ)

What is the derivative of-7csc(x+1/(x^5)) ?
The derivative of-7csc(x+1/(x^5)) is 7cot(x)csc(x)-5/(x^6)
What is the first derivative of-7csc(x+1/(x^5)) ?
The first derivative of-7csc(x+1/(x^5)) is 7cot(x)csc(x)-5/(x^6)