What is the derivative of 0.2x^3*3^x ?

The derivative of 0.2x^3*3^x is 0.2(3^{1+x}x^2+ln(3)*3^xx^3)

What is the first derivative of 0.2x^3*3^x ?

The first derivative of 0.2x^3*3^x is 0.2(3^{1+x}x^2+ln(3)*3^xx^3)

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derivative of

0.2 x^{3} \cdot 3^{x}

0.2 (3^{1 + x} x^{2} + ln (3) \cdot 3^{x} x^{3})

Solution steps

\frac{d}{d x} (0.2 x^{3} \cdot 3^{x})

Take the constant out:

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

= 0.2 \frac{d}{d x} (x^{3} \cdot 3^{x})

Apply the Product Rule:

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

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

= 0.2 (\frac{d}{d x} (x^{3}) 3^{x} + \frac{d}{d x} (3^{x}) x^{3})

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

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

= 0.2 (3 x^{2} \cdot 3^{x} + 3^{x} ln (3) x^{3})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3 \cdot 3^{x} = 3^{1 + x}

= 0.2 (3^{1 + x} x^{2} + ln (3) \cdot 3^{x} x^{3})

x \to \infty lim (- 1^{2 x})

\int e^{a}

\int (x + \frac{sin ( 2 x )}{y}) d x

f (x) = (8 x - 7)^{\frac{1}{2}}

\frac{d y}{d x} = e^{4 x + 5 y}

What is the derivative of 0.2x^3*3^x ?
The derivative of 0.2x^3*3^x is 0.2(3^{1+x}x^2+ln(3)*3^xx^3)
What is the first derivative of 0.2x^3*3^x ?
The first derivative of 0.2x^3*3^x is 0.2(3^{1+x}x^2+ln(3)*3^xx^3)