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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

derivative of (8x/(e^x))

\frac{d}{d x} (\frac{8 x}{e ^{x}})

area y=e^{2x},y=e^{-2x},x=1 area

y = e^{2 x}, y = e^{- 2 x}, x = 1

derivative of y=(f(x))/(g(x))derivative of

y = \frac{f ( x )}{g ( x )}

(\partial)/(\partial y)(x^2y+4y-7)

\frac{\partial}{\partial y} (x^{2} y + 4 y - 7)

f(x)=(2x-3)^{ln(x)}

f (x) = (2 x - 3)^{l n (x)}

Frequently Asked Questions (FAQ)

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