What is the derivative of x^{sec(x}) ?

The derivative of x^{sec(x}) is x^{sec(x)}(sec(x)tan(x)ln(x)+(sec(x))/x)

What is the first derivative of x^{sec(x}) ?

The first derivative of x^{sec(x}) is x^{sec(x)}(sec(x)tan(x)ln(x)+(sec(x))/x)

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\frac{d}{d x} (x^{s e c (x)})

x^{s e c (x)} (sec (x) tan (x) ln (x) + \frac{sec ( x )}{x})

Solution steps

\frac{d}{d x} (x^{s e c (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{s e c (x)} = e^{s e c (x) l n (x)}

= \frac{d}{d x} (e^{s e c (x) l n (x)})

Apply the chain rule:

e^{s e c (x) l n (x)} \frac{d}{d x} (sec (x) ln (x))

= e^{s e c (x) l n (x)} \frac{d}{d x} (sec (x) ln (x))

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

= e^{s e c (x) l n (x)} (sec (x) tan (x) ln (x) + \frac{sec ( x )}{x})

e^{s e c (x) l n (x)} = x^{s e c (x)}

= x^{s e c (x)} (sec (x) tan (x) ln (x) + \frac{sec ( x )}{x})

\int \frac{ln ( ln ( 5 x ) )}{5 x} d x

(x^{2} + 6)^{9}

\frac{\partial}{\partial z} (- x y)

t y^{^{''}} + y^{^{'}} = 0

f (x) = 7 x - 4 x^{2}, (- 3, - 57)

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