What is the derivative of sech(x-3ln(x)) ?

The derivative of sech(x-3ln(x)) is -sech(x-3)tanh(x-3)ln(x)+(sech(x-3))/x

What is the first derivative of sech(x-3ln(x)) ?

The first derivative of sech(x-3ln(x)) is -sech(x-3)tanh(x-3)ln(x)+(sech(x-3))/x

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\frac{d}{d x} (sech (x - 3) ln (x))

- sech (x - 3) tanh (x - 3) ln (x) + \frac{sech ( x - 3 )}{x}

Solution steps

\frac{d}{d x} (sech (x - 3) ln (x))

Apply the Product Rule:

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

f = sech (x - 3), g = ln (x)

= \frac{d}{d x} (sech (x - 3)) ln (x) + \frac{d}{d x} (ln (x)) sech (x - 3)

\frac{d}{d x} (sech (x - 3)) = - sech (x - 3) tanh (x - 3)

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

= (- sech (x - 3) tanh (x - 3)) ln (x) + \frac{1}{x} sech (x - 3)

Simplify

(- sech (x - 3) tanh (x - 3)) ln (x) + \frac{1}{x} sech (x - 3) : - sech (x - 3) tanh (x - 3) ln (x) + \frac{sech ( x - 3 )}{x}

= - sech (x - 3) tanh (x - 3) ln (x) + \frac{sech ( x - 3 )}{x}

\int \frac{3}{x ( 1 + 3 x ) ^{2}} d x

\int \frac{x}{a ^{4} - x ^{4}} d x

y = 5 x - x^{2}

x \to \infty lim (2 x + \frac{1}{x})

\int_{\frac{3}{2}}^{3} 9 - x^{2} d x

What is the derivative of sech(x-3ln(x)) ?
The derivative of sech(x-3ln(x)) is -sech(x-3)tanh(x-3)ln(x)+(sech(x-3))/x
What is the first derivative of sech(x-3ln(x)) ?
The first derivative of sech(x-3ln(x)) is -sech(x-3)tanh(x-3)ln(x)+(sech(x-3))/x