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

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

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

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

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derivative of

y = 3^{x^{2} + 3 x}

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

\frac{d}{d y} (\frac{y ^{3}}{27} + \frac{9}{4 y})

sin (4 x) + sin^{2} (4 x)

f (x) = - 3 lo g_{10} (x)

f (x) = - 2 x

f^{^{'}} (x) = 5 x^{2} + 7

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