What is the derivative of x(a+bxe^{3x}) ?

The derivative of x(a+bxe^{3x}) is ae^{3x}+2be^{3x}x+3ae^{3x}x+3be^{3x}x^2

What is the first derivative of x(a+bxe^{3x}) ?

The first derivative of x(a+bxe^{3x}) is ae^{3x}+2be^{3x}x+3ae^{3x}x+3be^{3x}x^2

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

a e^{3 x} + 2 b e^{3 x} x + 3 a e^{3 x} x + 3 b e^{3 x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((a + b x) e^{3 x}) = b e^{3 x} + e^{3 x} \cdot 3 (a + b x)

= 1 \cdot (a + b x) e^{3 x} + (b e^{3 x} + e^{3 x} \cdot 3 (a + b x)) x

Simplify

1 \cdot (a + b x) e^{3 x} + (b e^{3 x} + e^{3 x} \cdot 3 (a + b x)) x : a e^{3 x} + 2 b e^{3 x} x + 3 a e^{3 x} x + 3 b e^{3 x} x^{2}

= a e^{3 x} + 2 b e^{3 x} x + 3 a e^{3 x} x + 3 b e^{3 x} x^{2}

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

\int 6 x^{5} e^{7 x^{6}} d x

\frac{d}{d x} (x^{\frac{2}{3}} (6 - x)^{\frac{1}{3}})

\int_{8}^{13} \frac{y}{y ^{2} - 4 y - 5} d y

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{2 t}

What is the derivative of x(a+bxe^{3x}) ?
The derivative of x(a+bxe^{3x}) is ae^{3x}+2be^{3x}x+3ae^{3x}x+3be^{3x}x^2
What is the first derivative of x(a+bxe^{3x}) ?
The first derivative of x(a+bxe^{3x}) is ae^{3x}+2be^{3x}x+3ae^{3x}x+3be^{3x}x^2