What is the derivative of e^x(3x+1^3) ?

The derivative of e^x(3x+1^3) is e^x(3x+1)^3+9(3x+1)^2e^x

What is the first derivative of e^x(3x+1^3) ?

The first derivative of e^x(3x+1^3) is e^x(3x+1)^3+9(3x+1)^2e^x

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

e^{x} (3 x + 1)^{3} + 9 (3 x + 1)^{2} e^{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = (3 x + 1)^{3}

= \frac{d}{d x} (e^{x}) (3 x + 1)^{3} + \frac{d}{d x} ((3 x + 1)^{3}) e^{x}

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

\frac{d}{d x} ((3 x + 1)^{3}) = 9 (3 x + 1)^{2}

= e^{x} (3 x + 1)^{3} + 9 (3 x + 1)^{2} e^{x}

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

f (x) = 3 x^{2} - ln (x)

\frac{2}{x}, 3

x^{2} y^{^{''}} + x y^{^{'}} - y = \frac{1}{x}

\frac{d y}{d x} = (\frac{4 y + 3}{8 x + 5})^{2}

What is the derivative of e^x(3x+1^3) ?
The derivative of e^x(3x+1^3) is e^x(3x+1)^3+9(3x+1)^2e^x
What is the first derivative of e^x(3x+1^3) ?
The first derivative of e^x(3x+1^3) is e^x(3x+1)^3+9(3x+1)^2e^x