What is the derivative of 3^xtan(ln(x)) ?

The derivative of 3^xtan(ln(x)) is ln(3)*3^xtan(ln(x))+(3^xsec^2(ln(x)))/x

What is the first derivative of 3^xtan(ln(x)) ?

The first derivative of 3^xtan(ln(x)) is ln(3)*3^xtan(ln(x))+(3^xsec^2(ln(x)))/x

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derivative of

3^{x} tan (ln (x))

ln (3) \cdot 3^{x} tan (ln (x)) + \frac{3 ^{x} sec ^{2} ( ln ( x ) )}{x}

Solution steps

\frac{d}{d x} (3^{x} tan (ln (x)))

Apply the Product Rule:

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

f = 3^{x}, g = tan (ln (x))

= \frac{d}{d x} (3^{x}) tan (ln (x)) + \frac{d}{d x} (tan (ln (x))) 3^{x}

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

\frac{d}{d x} (tan (ln (x))) = \frac{sec ^{2} ( ln ( x ) )}{x}

= 3^{x} ln (3) tan (ln (x)) + \frac{sec ^{2} ( ln ( x ) )}{x} \cdot 3^{x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (3) \cdot 3^{x} tan (ln (x)) + \frac{3 ^{x} sec ^{2} ( ln ( x ) )}{x}

What is the derivative of 3^xtan(ln(x)) ?
The derivative of 3^xtan(ln(x)) is ln(3)*3^xtan(ln(x))+(3^xsec^2(ln(x)))/x
What is the first derivative of 3^xtan(ln(x)) ?
The first derivative of 3^xtan(ln(x)) is ln(3)*3^xtan(ln(x))+(3^xsec^2(ln(x)))/x