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Popular >

derivative of f(x)=tan(x)-1sec(x)

Solution

derivative of

f (x) = tan (x) - 1 sec (x)

Solution

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

Solution steps

\frac{d}{d x} (tan (x) - 1 \cdot sec (x))

Simplify

tan (x) - 1 \cdot sec (x) : tan (x) - sec (x)

= \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

derivative of f(x)=\sqrt[3]{x+2}derivative of

(\partial)/(\partial x)(ln(13x^2-10y^2))

\frac{\partial}{\partial x} (ln (13 x^{2} - 10 y^{2}))

(\partial)/(\partial x)(x^2y^3sin(x-2y))

\frac{\partial}{\partial x} (x^{2} y^{3} sin (x - 2 y))

derivative of (2xcos(x^2)/(sin(x^2)+1))

\frac{d}{d x} (\frac{2 x cos ( x ^{2} )}{sin ( x ^{2} ) + 1})

integral of x/(sqrt(a^2-x^2))

\int \frac{x}{a ^{2} - x ^{2}} d x

Frequently Asked Questions (FAQ)

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