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Find the derivative of $\mathrm{tanh}\left(3x^2+5x\right)$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$\mathrm{sech}\left(3x^2+5x\right)^2\left(6x+5\right)$
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Step-by-step Solution

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

Taking the derivative of hyperbolic tangent

Learn how to solve sum rule of differentiation problems step by step online.

$\mathrm{sech}\left(3x^2+5x\right)^2\frac{d}{dx}\left(3x^2+5x\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative of tanh(3x^2+5x). Taking the derivative of hyperbolic tangent. 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. The derivative of the linear function is equal to 1.

Final answer to the problem

$\mathrm{sech}\left(3x^2+5x\right)^2\left(6x+5\right)$

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Function Plot

Plotting: $\mathrm{sech}\left(3x^2+5x\right)^2\left(6x+5\right)$

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1
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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻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:

Similar Problems Solved

Find the derivative

$\frac{d}{dx}\left(x^2+y^2\right)$

$\frac{d}{dx}\left(\arctan\left(x-\sqrt{1+x^2}\right)\right)$

$\frac{d}{dx}\arctan\left(x-\sqrt{1+x^2}\right)$

$\frac{d}{dx}\arccos\left(\sqrt{1-x^2}\right)$

$\frac{d}{dx}\left(\cosh\left(x^5\right)\right)$

$\frac{d}{dx}\left(\sinh^2\left(7x\right)\right)$

Find the derivative

$\frac{d}{dx}\left(x\sinh x-\cosh x\right)$

Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Used Formulas

See formulas (4)

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