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

Step-by-step Solution

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Final answer to the problem

$5\left(\cos\left(x\right)\ln\left(x\right)+\frac{\sin\left(x\right)}{x}\right)x^{5\sin\left(x\right)}$
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Step-by-step Solution

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Apply the formula: $\frac{d}{dx}\left(a^b\right)$$=y=a^b$, where $d/dx=\frac{d}{dx}$, $a=x$, $b=5\sin\left(x\right)$, $a^b=x^{5\sin\left(x\right)}$ and $d/dx?a^b=\frac{d}{dx}\left(x^{5\sin\left(x\right)}\right)$

$y=x^{5\sin\left(x\right)}$

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$y=x^{5\sin\left(x\right)}$

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Learn how to solve problems step by step online. d/dx(x^(5sin(x))). Apply the formula: \frac{d}{dx}\left(a^b\right)=y=a^b, where d/dx=\frac{d}{dx}, a=x, b=5\sin\left(x\right), a^b=x^{5\sin\left(x\right)} and d/dx?a^b=\frac{d}{dx}\left(x^{5\sin\left(x\right)}\right). Apply the formula: y=a^b\to \ln\left(y\right)=\ln\left(a^b\right), where a=x and b=5\sin\left(x\right). Apply the formula: \ln\left(x^a\right)=a\ln\left(x\right), where a=5\sin\left(x\right). Apply the formula: \ln\left(y\right)=x\to \frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(x\right), where x=5\sin\left(x\right)\ln\left(x\right).

Final answer to the problem

$5\left(\cos\left(x\right)\ln\left(x\right)+\frac{\sin\left(x\right)}{x}\right)x^{5\sin\left(x\right)}$

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Plotting: $5\left(\cos\left(x\right)\ln\left(x\right)+\frac{\sin\left(x\right)}{x}\right)x^{5\sin\left(x\right)}$

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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
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

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