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# Find the derivative of $5x^{\cos\left(2x\right)}$

## Step-by-step Solution

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###  Solution

$5\left(-2x\sin\left(2x\right)\ln\left(x\right)+\cos\left(2x\right)\right)x^{\left(\cos\left(2x\right)-1\right)}$
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##  Step-by-step Solution 

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1

The derivative of a function multiplied by a constant ($5$) is equal to the constant times the derivative of the function

$5\frac{d}{dx}\left(x^{\cos\left(2x\right)}\right)$
2

The derivative $\frac{d}{dx}\left(x^{\cos\left(2x\right)}\right)$ results in $\left(-2x\sin\left(2x\right)\ln\left(x\right)+\cos\left(2x\right)\right)x^{\left(\cos\left(2x\right)-1\right)}$

$5\left(-2x\sin\left(2x\right)\ln\left(x\right)+\cos\left(2x\right)\right)x^{\left(\cos\left(2x\right)-1\right)}$

$5\left(-2x\sin\left(2x\right)\ln\left(x\right)+\cos\left(2x\right)\right)x^{\left(\cos\left(2x\right)-1\right)}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of 5x^cos2x using the product ruleFind derivative of 5x^cos2x using the quotient ruleFind derivative of 5x^cos2x using logarithmic differentiationFind derivative of 5x^cos2x using the definition

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7
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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
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