What is the derivative of 3^{sqrt(x^2+1)} ?

The derivative of 3^{sqrt(x^2+1)} is (ln(3)*3^{sqrt(x^2+1)}x)/(sqrt(x^2+1))

What is the first derivative of 3^{sqrt(x^2+1)} ?

The first derivative of 3^{sqrt(x^2+1)} is (ln(3)*3^{sqrt(x^2+1)}x)/(sqrt(x^2+1))

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derivative of

3^{x^{2} + 1}

\frac{ln ( 3 ) \cdot 3 ^{x^{2} + 1} x}{x ^{2} + 1}

Solution steps

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

Apply exponent rule:

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

3^{x^{2} + 1} = e^{x^{2} + 1 l n (3)}

= \frac{d}{d x} (e^{x^{2} + 1 l n (3)})

Apply the chain rule:

e^{x^{2} + 1 l n (3)} \frac{d}{d x} (x^{2} + 1 ln (3))

= e^{x^{2} + 1 l n (3)} \frac{d}{d x} (x^{2} + 1 ln (3))

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

= e^{x^{2} + 1 l n (3)} \frac{ln ( 3 ) x}{x ^{2} + 1}

Simplify

e^{x^{2} + 1 l n (3)} \frac{ln ( 3 ) x}{x ^{2} + 1} : \frac{ln ( 3 ) \cdot 3 ^{x^{2} + 1} x}{x ^{2} + 1}

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

What is the derivative of 3^{sqrt(x^2+1)} ?
The derivative of 3^{sqrt(x^2+1)} is (ln(3)*3^{sqrt(x^2+1)}x)/(sqrt(x^2+1))
What is the first derivative of 3^{sqrt(x^2+1)} ?
The first derivative of 3^{sqrt(x^2+1)} is (ln(3)*3^{sqrt(x^2+1)}x)/(sqrt(x^2+1))