What is (\partial)/(\partial x)(sec(x)tan(x)) ?

The answer to (\partial)/(\partial x)(sec(x)tan(x)) is -sec(x)+2sec^3(x)

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(\partial)/(\partial x)(sec(x)tan(x))

\frac{\partial}{\partial x} (sec (x) tan (x))

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

Solution steps

\frac{\partial}{\partial x} (sec (x) tan (x))

Apply the Product Rule:

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

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

= \frac{\partial}{\partial x} (sec (x)) tan (x) + \frac{\partial}{\partial x} (tan (x)) sec (x)

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

\frac{\partial}{\partial 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)

y^{^{'}} = 5 y^{\frac{1}{5}}

\frac{d}{d x} (3 x + \frac{6}{x})

\frac{d}{d x} (\frac{1}{2} sin (x))

\int (e^{x} - 3)^{4} e^{x} d x

\int_{2}^{3} 3 x 2 x^{2} - 1 d x

What is (\partial)/(\partial x)(sec(x)tan(x)) ?
The answer to (\partial)/(\partial x)(sec(x)tan(x)) is -sec(x)+2sec^3(x)