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Popular >

derivative of 7arctanh(cos(x))

Solution

\frac{d}{d x} (7 arctanh (cos (x)))

Solution

- 7 csc (x)

Solution steps

\frac{d}{d x} (7 arctanh (cos (x)))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (arctanh (cos (x)))

Apply the chain rule:

\frac{1}{1 - ( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

= \frac{1}{1 - ( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= 7 \cdot \frac{1}{1 - ( cos ( x ) ) ^{2}} (- sin (x))

Simplify

7 \cdot \frac{1}{1 - cos ^{2} ( x )} (- sin (x)) : - 7 csc (x)

= - 7 csc (x)

Popular Examples

limit as x approaches 2 of (x^4-16)/(x^3-8)

x \to 2 lim (\frac{x ^{4} - 16}{x ^{3} - 8})

integral of e^{2x}-1

\int e^{2 x} - 1 d x

integral of (5x^2)/((121+x^2)^2)

\int \frac{5 x ^{2}}{( 121 + x ^{2} ) ^{2}} d x

limit as x approaches 1 of 1/(ln(x))

x \to 1 lim (\frac{1}{ln ( x )})

integral of 7e^x-3

\int 7 e^{x} - 3 d x

Frequently Asked Questions (FAQ)

What is the derivative of 7arctanh(cos(x)) ?
The derivative of 7arctanh(cos(x)) is -7csc(x)
What is the first derivative of 7arctanh(cos(x)) ?
The first derivative of 7arctanh(cos(x)) is -7csc(x)