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Popular >

derivative of sqrt(tan^2(3x+1))

Solution

\frac{d}{d x} (tan^{2} (3 x) + 1)

Solution

3 sec (3 x) tan (3 x)

Solution steps

\frac{d}{d x} (tan^{2} (3 x) + 1)

Apply the chain rule:

\frac{1}{2 tan ^{2} ( 3 x ) + 1} \frac{d}{d x} (tan^{2} (3 x) + 1)

= \frac{1}{2 tan ^{2} ( 3 x ) + 1} \frac{d}{d x} (tan^{2} (3 x) + 1)

\frac{d}{d x} (tan^{2} (3 x) + 1) = 6 sec^{2} (3 x) tan (3 x)

= \frac{1}{2 tan ^{2} ( 3 x ) + 1} \cdot 6 sec^{2} (3 x) tan (3 x)

Simplify

\frac{1}{2 tan ^{2} ( 3 x ) + 1} \cdot 6 sec^{2} (3 x) tan (3 x) : 3 sec (3 x) tan (3 x)

= 3 sec (3 x) tan (3 x)

Graph

Popular Examples

integral of t^2e^{-t/3}

\int t^{2} e^{- \frac{t}{3}} d t

sum from n=7 to infinity of 1/(6n)

n = 7 \sum \infty \frac{1}{6 n}

slope of y=x^2+5x,x=8 slope

y = x^{2} + 5 x, x = 8

integral of (x^2-2x+3)

\int (x^{2} - 2 x + 3) d x

integral of (3x^3)/(x^2+1)

\int \frac{3 x ^{3}}{x ^{2} + 1} d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(tan^2(3x+1)) ?
The derivative of sqrt(tan^2(3x+1)) is 3sec(3x)tan(3x)
What is the first derivative of sqrt(tan^2(3x+1)) ?
The first derivative of sqrt(tan^2(3x+1)) is 3sec(3x)tan(3x)