What is the derivative of ln(3^{x^2}) ?

The derivative of ln(3^{x^2}) is 2ln(3)x

What is the first derivative of ln(3^{x^2}) ?

The first derivative of ln(3^{x^2}) is 2ln(3)x

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\frac{d}{d x} (ln (3^{x^{2}}))

2 ln (3) x

Solution steps

\frac{d}{d x} (ln (3^{x^{2}}))

Simplify

ln (3^{x^{2}}) : ln (3) x^{2}

= \frac{d}{d x} (ln (3) x^{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= ln (3) \frac{d}{d x} (x^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= ln (3) \cdot 2 x^{2 - 1}

Simplify

= 2 ln (3) x

x \to 4 lim (3 x^{3} - 2 x^{2} + x - 7)

\frac{( 3 x ^{2} )}{4} + \frac{x}{3}

\int \frac{3 - 18 x}{25 - 9 x ^{2}} d x

ln (\frac{4 x}{x + 7})

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

What is the derivative of ln(3^{x^2}) ?
The derivative of ln(3^{x^2}) is 2ln(3)x
What is the first derivative of ln(3^{x^2}) ?
The first derivative of ln(3^{x^2}) is 2ln(3)x