What is the derivative of f(x)=(x^2+3x+5)e^{6x} ?

The derivative of f(x)=(x^2+3x+5)e^{6x} is 6e^{6x}x^2+20e^{6x}x+33e^{6x}

What is the first derivative of f(x)=(x^2+3x+5)e^{6x} ?

The first derivative of f(x)=(x^2+3x+5)e^{6x} is 6e^{6x}x^2+20e^{6x}x+33e^{6x}

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derivative of

f (x) = (x^{2} + 3 x + 5) e^{6 x}

6 e^{6 x} x^{2} + 20 e^{6 x} x + 33 e^{6 x}

Solution steps

\frac{d}{d x} ((x^{2} + 3 x + 5) e^{6 x})

Apply the Product Rule:

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

f = x^{2} + 3 x + 5, g = e^{6 x}

= \frac{d}{d x} (x^{2} + 3 x + 5) e^{6 x} + \frac{d}{d x} (e^{6 x}) (x^{2} + 3 x + 5)

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

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= (2 x + 3) e^{6 x} + e^{6 x} \cdot 6 (x^{2} + 3 x + 5)

Simplify

(2 x + 3) e^{6 x} + e^{6 x} \cdot 6 (x^{2} + 3 x + 5) : 6 e^{6 x} x^{2} + 20 e^{6 x} x + 33 e^{6 x}

= 6 e^{6 x} x^{2} + 20 e^{6 x} x + 33 e^{6 x}

\frac{d}{d t} (2 - 2 t)

\int \frac{csc ^{2} ( x )}{cot ^{2} ( x )} d x

\int_{0}^{2} \frac{e ^{x}}{1 + e ^{x}} d x

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

30 y^{^{''}} - 19 y^{^{'}} - 5 y = 0

What is the derivative of f(x)=(x^2+3x+5)e^{6x} ?
The derivative of f(x)=(x^2+3x+5)e^{6x} is 6e^{6x}x^2+20e^{6x}x+33e^{6x}
What is the first derivative of f(x)=(x^2+3x+5)e^{6x} ?
The first derivative of f(x)=(x^2+3x+5)e^{6x} is 6e^{6x}x^2+20e^{6x}x+33e^{6x}