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Popular >

derivative of (csc(x*tan(x))/(cos(x)))

Solution

\frac{d}{d x} (\frac{csc ( x ) \cdot tan ( x )}{cos ( x )})

Solution

2 sec^{2} (x) tan (x)

Solution steps

\frac{d}{d x} (\frac{csc ( x ) tan ( x )}{cos ( x )})

Simplify

\frac{csc ( x ) tan ( x )}{cos ( x )} : sec^{2} (x)

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

Apply the chain rule:

2 sec (x) \frac{d}{d x} (sec (x))

= 2 sec (x) \frac{d}{d x} (sec (x))

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= 2 sec (x) sec (x) tan (x)

Simplify

2 sec (x) sec (x) tan (x) : 2 sec^{2} (x) tan (x)

= 2 sec^{2} (x) tan (x)

Popular Examples

(\partial)/(\partial x)((1-x^2-y^2)^{1/2})

\frac{\partial}{\partial x} ((1 - x^{2} - y^{2})^{\frac{1}{2}})

limit as x approaches pi/2+of 9/x sec(x)

x \to \frac{π}{2} + lim (\frac{9}{x} sec (x))

(\partial)/(\partial y)(e^zcos(y))

\frac{\partial}{\partial y} (e^{z} cos (y))

tangent of f(x)=(10)/(1+e^{-x)},\at x=0 tangent of

f (x) = \frac{10}{1 + e ^{- x}}, at x = 0

sum from n=2 to infinity of ((n+1)/n)^n

n = 2 \sum \infty (\frac{n + 1}{n})^{n}

Frequently Asked Questions (FAQ)

What is the derivative of (csc(x*tan(x))/(cos(x))) ?
The derivative of (csc(x*tan(x))/(cos(x))) is 2sec^2(x)tan(x)
What is the first derivative of (csc(x*tan(x))/(cos(x))) ?
The first derivative of (csc(x*tan(x))/(cos(x))) is 2sec^2(x)tan(x)