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

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

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

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

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derivative of

f (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)

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

f (x) = x^{2} - x + 7, at x = 2

x y - 5 y^{2} = 4 (12.2)

\int_{- 3}^{4} \frac{8}{x ^{3}} d x

\frac{d y}{d x} + \frac{1}{x} y = 5 x^{2}

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