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Find the derivative of $\ln\left(\mathrm{cosh}\left(6x+3\right)\right)$

Step-by-step Solution

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Solution

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Final answer to the problem

$6\mathrm{tanh}\left(6x+3\right)$
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Step-by-step Solution

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Learn how to solve definite integrals problems step by step online. Find the derivative of ln(cosh(6x+3)). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Taking the derivative of hyperbolic cosine. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function times a constant, is equal to the constant.

Final answer to the problem

$6\mathrm{tanh}\left(6x+3\right)$

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Function Plot

Plotting: $6\mathrm{tanh}\left(6x+3\right)$

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ln
log
log◻
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d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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