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Popular >

derivative of (sec(x+csc(x))/(csc(x)))

Solution

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

Solution

sec^{2} (x)

Solution steps

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

Simplify

\frac{sec ( x ) + csc ( x )}{csc ( x )} : 1 + tan (x)

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (1) = 0

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

= 0 + sec^{2} (x)

Simplify

= sec^{2} (x)

Popular Examples

integral of cos(x)(tan(x)+sec(x))

\int cos (x) (tan (x) + sec (x)) d x

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

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

d/(d{x)}(sqrt(25-{x)^2-{y}^2-{z}^2})

\frac{d}{d x} (25 - x^{2} - y^{2} - z^{2})

(\partial)/(\partial x)(x^2ye^{x-z})

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

inverse oflaplace 1/(1+s)*8/s inverse laplace

\frac{1}{1 + s} \cdot \frac{8}{s}

Frequently Asked Questions (FAQ)

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