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Popular >

derivative of (e^x/(cos(x)))

Solution

\frac{d}{d x} (\frac{e ^{x}}{cos ( x )})

Solution

\frac{e ^{x} + e ^{x} tan ( x )}{cos ( x )}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{cos ( x )})

Simplify

\frac{e ^{x}}{cos ( x )} : e^{x} sec (x)

= \frac{d}{d x} (e^{x} sec (x))

Apply the Product Rule:

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

f = e^{x}, g = sec (x)

= \frac{d}{d x} (e^{x}) sec (x) + \frac{d}{d x} (sec (x)) e^{x}

\frac{d}{d x} (e^{x}) = e^{x}

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

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

Rewrite using trig identities

= \frac{e ^{x} + e ^{x} tan ( x )}{cos ( x )}

Popular Examples

taylor x^3-4sqrt(x)+log_{e}(x)taylor

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(\partial)/(\partial x)(-3xy^2+2ycos(x))

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

(\partial)/(\partial y)(2(y+1)x^2)

\frac{\partial}{\partial y} (2 (y + 1) x^{2})

integral of-1/2 x^3e^{-x}

\int - \frac{1}{2} x^{3} e^{- x} d x

integral of v/(sqrt(1+v^2))

\int \frac{v}{1 + v ^{2}} d v

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(cos(x))) ?
The derivative of (e^x/(cos(x))) is (e^x+e^xtan(x))/(cos(x))
What is the first derivative of (e^x/(cos(x))) ?
The first derivative of (e^x/(cos(x))) is (e^x+e^xtan(x))/(cos(x))