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Find the derivative $\frac{d}{dx}\left(\frac{\sqrt{\sin\left(x\right)^5\ln\left(x\right)}}{\sec\left(x\right)^2}\right)$

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Solution

Formulas

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Basic Derivatives

· Quotient Rule in Differentiation
$\frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$
· Product rule for derivatives
$\frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right)$
· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Derivatives of trigonometric functions

· Derivative of the sine function
$\frac{d}{dx}\left(\sin\left(\theta \right)\right)=\cos\left(\theta \right)$
· Derivative of secant function
$\frac{d}{dx}\left(\sec\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\sec\left(\theta \right)\tan\left(\theta \right)$

Function Plot

Plotting: $\frac{\left(\frac{5}{2}\sqrt{\ln\left(x\right)}\sqrt{\sin\left(x\right)^{3}}\cos\left(x\right)+\frac{\sqrt{\sin\left(x\right)^{5}}}{2x\sqrt{\ln\left(x\right)}}\right)\sec\left(x\right)^2-2\sqrt{\ln\left(x\right)}\sec\left(x\right)^2\sqrt{\sin\left(x\right)^{5}}\tan\left(x\right)}{\sec\left(x\right)^{4}}$

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0
a
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m
n
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v
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x
y
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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

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Main Topic: Quotient Rule of Differentiation

The quotient rule is a formal rule for differentiating problems where one function is divided by another.

Used Formulas

6. See formulas

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