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Popular >

derivative of (csc(xtan(x))/(cos(x)))

Solution

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

integral of sin^4(x)*cos(x)

\int sin^{4} (x) \cdot cos (x) d x

area x,sqrt(x),[0,2]area

x, x, [0, 2]

tangent of f(x)=sqrt(x^2-6x+25),\at x=0 tangent of

f (x) = x^{2} - 6 x + 25, at x = 0

tangent of f(x)=x^4+7e^x,(0,7)tangent of

f (x) = x^{4} + 7 e^{x}, (0, 7)

integral of (9sin^3(x))/(cos(x))

\int \frac{9 sin ^{3} ( x )}{cos ( x )} d x

Frequently Asked Questions (FAQ)

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