What is the derivative of e^x(2x+3^3) ?

The derivative of e^x(2x+3^3) is e^x(2x+3)^3+6(2x+3)^2e^x

What is the first derivative of e^x(2x+3^3) ?

The first derivative of e^x(2x+3^3) is e^x(2x+3)^3+6(2x+3)^2e^x

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

e^{x} (2 x + 3)^{3} + 6 (2 x + 3)^{2} e^{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = (2 x + 3)^{3}

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

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} ((2 x + 3)^{3}) = 6 (2 x + 3)^{2}

= e^{x} (2 x + 3)^{3} + 6 (2 x + 3)^{2} e^{x}

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

\int \frac{9 x}{x ^{2} + 1} d x

f (x) = 6 x, at x = 1

(16 y^{2} - x y) d x + x^{2} d y = 0

What is the derivative of e^x(2x+3^3) ?
The derivative of e^x(2x+3^3) is e^x(2x+3)^3+6(2x+3)^2e^x
What is the first derivative of e^x(2x+3^3) ?
The first derivative of e^x(2x+3^3) is e^x(2x+3)^3+6(2x+3)^2e^x