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Popular >

derivative of e^xsec(x)

Solution

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

Solution

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

Solution steps

\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

integral of (sin^3(x))/(cos^3(x))

\int \frac{sin ^{3} ( x )}{cos ^{3} ( x )} d x

derivative of 8x^{1/2}

\frac{d}{d x} (8 x^{\frac{1}{2}})

derivative of 15e^{1/x}

\frac{d}{d x} (15 e^{\frac{1}{x}})

limit as x approaches 0+of xln(tan(9x))

x \to 0 + lim (x ln (tan (9 x)))

d y - (y - 2)^{2} d x = 0

Frequently Asked Questions (FAQ)

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