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Popular >

(sec(x)tan(x))^'

Solution

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

Solution

- sec (x) + 2 sec^{3} (x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec (x), g = tan (x)

= (sec (x))^{^{'}} tan (x) + (tan (x))^{^{'}} sec (x)

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

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

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

Simplify

sec (x) tan (x) tan (x) + sec^{2} (x) sec (x) : - sec (x) + 2 sec^{3} (x)

= - sec (x) + 2 sec^{3} (x)

Popular Examples

derivative of (3(7x^2-2x+6))/(4x^{5/2)}derivative of

\frac{3 ( 7 x ^{2} - 2 x + 6 )}{4 x ^{\frac{5}{2}}}

(\partial)/(\partial x)(xye^z)

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

derivative of y=2sin(2x)derivative of

y = 2 sin (2 x)

(\partial)/(\partial x)(xye^2)

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

integral from 1 to 3 of (x+2)^3

\int_{1}^{3} (x + 2)^{3} d x

Frequently Asked Questions (FAQ)

What is the (sec(x)tan(x))^' ?
The (sec(x)tan(x))^' is -sec(x)+2sec^3(x)
What is the first (sec(x)tan(x))^' ?
The first (sec(x)tan(x))^' is -sec(x)+2sec^3(x)