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Find the derivative of $5\cdot \left(\frac{\sin\left(2\right)}{\cos\left(2\right)}\right)\tan\left(2x\right)^5$

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Solution

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Final answer to the problem

$50\sec\left(2\right)\sin\left(2\right)\tan\left(2x\right)^{4}\sec\left(2x\right)^2$
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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
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Simplify the derivative by applying the properties of logarithms

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

Learn how to solve differential calculus problems step by step online.

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

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Learn how to solve differential calculus problems step by step online. Find the derivative of 5tan(2x)^5sin(2)/cos(2). Simplify the derivative by applying the properties of logarithms. The derivative of a function multiplied by a constant (\frac{1}{\cos\left(2\right)}) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

Final answer to the problem

$50\sec\left(2\right)\sin\left(2\right)\tan\left(2x\right)^{4}\sec\left(2x\right)^2$

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Plotting: $50\sec\left(2\right)\sin\left(2\right)\tan\left(2x\right)^{4}\sec\left(2x\right)^2$

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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

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$\frac{d}{dx}\left(x^{\frac{3}{4}}\right)$

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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