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

## Step-by-step Solution

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### Videos

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

Problem to solve:

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

Specify the solving method

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.

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

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)}.

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

### Explore different ways to solve this problem

Find the derivativeProduct ruleQuotient ruleLogarithmic differentiation
SnapXam A2

### beta Got another answer? Verify it!

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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

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

### Main topic:

Differential Calculus

~ 0.05 s