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

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

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

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

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

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

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)) = 2 ln (3) x

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

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

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

\int \frac{3}{x} + 1 d x

y = 4 (x - 1 x) 4, at x = 2

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

\int 4 z + z 1 - z^{2} d z

- 5 e^{x}

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