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

The derivative of 3^{2x^2+3x-1} is ln(3)*3^{2x^2+3x-1}(4x+3)

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

The first derivative of 3^{2x^2+3x-1} is ln(3)*3^{2x^2+3x-1}(4x+3)

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

ln (3) \cdot 3^{2 x^{2} + 3 x - 1} (4 x + 3)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} ((2 x^{2} + 3 x - 1) ln (3)) = ln (3) (4 x + 3)

= e^{(2 x^{2} + 3 x - 1) l n (3)} ln (3) (4 x + 3)

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

= ln (3) \cdot 3^{2 x^{2} + 3 x - 1} (4 x + 3)

e^{- y} sin (x) - y^{^{'}} cos^{2} (x) = 0

\frac{d}{d x} (- 0.8 sin (x) + cos (2 x))

y^{^{'}} = y (x y^{5} + 3)

x \to 8 lim (500 x - 6 x^{2})

x \to 4 - lim (\frac{x}{x - 4})

What is the derivative of 3^{2x^2+3x-1} ?
The derivative of 3^{2x^2+3x-1} is ln(3)*3^{2x^2+3x-1}(4x+3)
What is the first derivative of 3^{2x^2+3x-1} ?
The first derivative of 3^{2x^2+3x-1} is ln(3)*3^{2x^2+3x-1}(4x+3)