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

Step-by-step Solution

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Solution

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Final Answer

$-109.251899\tan\left(2x\right)^{4}\sec\left(2x\right)^2$
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Step-by-step Solution

Problem to solve:

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

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1

Simplifying

$\frac{d}{dx}\left(-10.92519\tan\left(2x\right)^5\right)$

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

$\frac{d}{dx}\left(-10.92519\tan\left(2x\right)^5\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of 5tan(2x)^5(sin(2)/(cos(2). Simplifying. The derivative of a function multiplied by a constant (-10.92519) 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}. The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}.

Final Answer

$-109.251899\tan\left(2x\right)^{4}\sec\left(2x\right)^2$

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 d/dx(5tan(2x)^5(sin(2)/(cos(2)) using the product ruleFind d/dx(5tan(2x)^5(sin(2)/(cos(2)) using the quotient ruleFind d/dx(5tan(2x)^5(sin(2)/(cos(2)) using logarithmic differentiation

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0
a
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m
n
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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

How to improve your answer:

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Main topic:

Differential Calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.04 s

Related topics:

Differential CalculusPower Rule for DerivativesBasic Differentiation Rules

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