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Popular >

derivative of ln(xsec(x))

Solution

\frac{d}{d x} (ln (x) sec (x))

Solution

\frac{sec ( x )}{x} + sec (x) tan (x) ln (x)

Solution steps

\frac{d}{d x} (ln (x) sec (x))

Apply the Product Rule:

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

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

= \frac{d}{d x} (ln (x)) sec (x) + \frac{d}{d x} (sec (x)) ln (x)

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

= \frac{1}{x} sec (x) + sec (x) tan (x) ln (x)

\frac{1}{x} sec (x) = \frac{sec ( x )}{x}

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

Popular Examples

(dy)/(dx)=3x^2-xy

\frac{d y}{d x} = 3 x^{2} - x y

integral of x^6cos(x)

\int x^{6} cos (x) d x

derivative of ln(cos(5x))derivative of

ln (cos (5 x))

y^{''}-5y^'+4y=0,y(0)=-5,y^'(0)=3

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = - 5, y^{^{'}} (0) = 3

limit as x approaches c of 9/8 (7/8)

x \to c lim (\frac{9}{8} (\frac{7}{8}))

Frequently Asked Questions (FAQ)

What is the derivative of ln(xsec(x)) ?
The derivative of ln(xsec(x)) is (sec(x))/x+sec(x)tan(x)ln(x)
What is the first derivative of ln(xsec(x)) ?
The first derivative of ln(xsec(x)) is (sec(x))/x+sec(x)tan(x)ln(x)