What is the derivative of 5x^2*2e^{3x} ?

The derivative of 5x^2*2e^{3x} is 10(e^{3x}*3x^2+2xe^{3x})

What is the first derivative of 5x^2*2e^{3x} ?

The first derivative of 5x^2*2e^{3x} is 10(e^{3x}*3x^2+2xe^{3x})

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

10 (e^{3 x} \cdot 3 x^{2} + 2 x e^{3 x})

Solution steps

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

Simplify

5 x^{2} \cdot 2 e^{3 x} : 10 e^{3 x} x^{2}

= \frac{d}{d x} (10 e^{3 x} x^{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (e^{3 x} x^{2})

Apply the Product Rule:

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

f = e^{3 x}, g = x^{2}

= 10 (\frac{d}{d x} (e^{3 x}) x^{2} + \frac{d}{d x} (x^{2}) e^{3 x})

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

\frac{d}{d x} (x^{2}) = 2 x

= 10 (e^{3 x} \cdot 3 x^{2} + 2 x e^{3 x})

\frac{e ^{- s}}{( s + 1 )}

\int sin (t - x) d x

x \to 0 + lim (coth (x))

\int - 4 x d x

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

What is the derivative of 5x^2*2e^{3x} ?
The derivative of 5x^2*2e^{3x} is 10(e^{3x}*3x^2+2xe^{3x})
What is the first derivative of 5x^2*2e^{3x} ?
The first derivative of 5x^2*2e^{3x} is 10(e^{3x}*3x^2+2xe^{3x})