What is the derivative of ln(cosh(7x)) ?

The derivative of ln(cosh(7x)) is 7tanh(7x)

What is the first derivative of ln(cosh(7x)) ?

The first derivative of ln(cosh(7x)) is 7tanh(7x)

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\frac{d}{d x} (ln (cosh (7 x)))

7 tanh (7 x)

Solution steps

\frac{d}{d x} (ln (cosh (7 x)))

Apply the chain rule:

\frac{1}{cosh ( 7 x )} \frac{d}{d x} (cosh (7 x))

= \frac{1}{cosh ( 7 x )} \frac{d}{d x} (cosh (7 x))

\frac{d}{d x} (cosh (7 x)) = sinh (7 x) \cdot 7

= \frac{1}{cosh ( 7 x )} sinh (7 x) \cdot 7

Simplify

\frac{1}{cosh ( 7 x )} sinh (7 x) \cdot 7 : 7 tanh (7 x)

= 7 tanh (7 x)

\int x^{2} + x^{2} d x

\int - k e^{- k x} d x

\int \frac{cos ( \frac{π}{x ^{33}} )}{x ^{34}} d x

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

\frac{\partial}{\partial x} (e^{\frac{x y}{z}})

What is the derivative of ln(cosh(7x)) ?
The derivative of ln(cosh(7x)) is 7tanh(7x)
What is the first derivative of ln(cosh(7x)) ?
The first derivative of ln(cosh(7x)) is 7tanh(7x)