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

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

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

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

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derivative of

x \cdot 3^{x^{2} + 1}

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = 3^{x^{2} + 1}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

6 (t + 1) (\frac{d y}{d t}) - 5 y = 5 t

x \to \frac{π}{2} lim (cos (3 x))

(1 + p^{2}) (x + e^{- x}) - 10

\int e^{x} sin^{2} (e^{x}) d x

y = x^{2}, y = x + 2, - 2, 2

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