What is the derivative of 3^{4x^2+3x} ?

The derivative of 3^{4x^2+3x} is ln(3)*3^{4x^2+3x}(8x+3)

What is the first derivative of 3^{4x^2+3x} ?

The first derivative of 3^{4x^2+3x} is ln(3)*3^{4x^2+3x}(8x+3)

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

ln (3) \cdot 3^{4 x^{2} + 3 x} (8 x + 3)

Solution steps

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

Apply exponent rule:

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

3^{4 x^{2} + 3 x} = e^{(4 x^{2} + 3 x) l n (3)}

= \frac{d}{d x} (e^{(4 x^{2} + 3 x) l n (3)})

Apply the chain rule:

e^{(4 x^{2} + 3 x) l n (3)} \frac{d}{d x} ((4 x^{2} + 3 x) ln (3))

= e^{(4 x^{2} + 3 x) l n (3)} \frac{d}{d x} ((4 x^{2} + 3 x) ln (3))

\frac{d}{d x} ((4 x^{2} + 3 x) ln (3)) = ln (3) (8 x + 3)

= e^{(4 x^{2} + 3 x) l n (3)} ln (3) (8 x + 3)

e^{(4 x^{2} + 3 x) l n (3)} = 3^{4 x^{2} + 3 x}

= ln (3) \cdot 3^{4 x^{2} + 3 x} (8 x + 3)

\frac{\partial}{\partial x} (2 e^{x^{2}})

x \to 0 lim (\frac{14}{x})

\frac{10}{( s \cdot ( s + 1 ) )}

x^{2} - 2 x, 4 x + 7

What is the derivative of 3^{4x^2+3x} ?
The derivative of 3^{4x^2+3x} is ln(3)*3^{4x^2+3x}(8x+3)
What is the first derivative of 3^{4x^2+3x} ?
The first derivative of 3^{4x^2+3x} is ln(3)*3^{4x^2+3x}(8x+3)