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Popular >

derivative of tan(x-sec(x))

Solution

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

Solution

\frac{1}{1 + sin ( x )}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

= \frac{1}{1 + sin ( x )}

Popular Examples

(\partial)/(\partial x)(x^3+y^3-9xy)

\frac{\partial}{\partial x} (x^{3} + y^{3} - 9 x y)

limit as x approaches pi/4 of tan(x)

x \to \frac{π}{4} lim (tan (x))

derivative of x/(sqrt(x)+9)derivative of

\frac{x}{x + 9}

tangent of y=e^{-4t},\at t=0 tangent of

y = e^{- 4 t}, at t = 0

derivative of (1+csc(x^7))/(1-cot(x^7))derivative of

\frac{1 + csc ( x ^{7} )}{1 - cot ( x ^{7} )}

Frequently Asked Questions (FAQ)

What is the derivative of tan(x-sec(x)) ?
The derivative of tan(x-sec(x)) is 1/(1+sin(x))
What is the first derivative of tan(x-sec(x)) ?
The first derivative of tan(x-sec(x)) is 1/(1+sin(x))