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Find the derivative of $\ln\left(\mathrm{sinh}\left(7x\right)\right)$

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{7\mathrm{cosh}\left(7x\right)}{\mathrm{sinh}\left(7x\right)}$
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Step-by-step Solution

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Learn how to solve basic differentiation rules problems step by step online. Find the derivative of ln(sinh(7x)). 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 sine. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1.

Final answer to the problem

$\frac{7\mathrm{cosh}\left(7x\right)}{\mathrm{sinh}\left(7x\right)}$

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Function Plot

Plotting: $\frac{7\mathrm{cosh}\left(7x\right)}{\mathrm{sinh}\left(7x\right)}$

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◻/◻
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◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
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

How to improve your answer:

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Main Topic: Basic Differentiation Rules

Some differentiation rules are very easy to remember and use. These are the basic ones: constant rule, sum rule, product rule and quotient rule.

Used Formulas

See formulas (3)

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