What is the derivative of 0.9x^33^x ?

The derivative of 0.9x^33^x is 0.9(3^{1+x}x^2+ln(3)*3^xx^3)

What is the first derivative of 0.9x^33^x ?

The first derivative of 0.9x^33^x is 0.9(3^{1+x}x^2+ln(3)*3^xx^3)

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derivative of

0.9 x^{3} 3^{x}

0.9 (3^{1 + x} x^{2} + ln (3) \cdot 3^{x} x^{3})

Solution steps

\frac{d}{d x} (0.9 x^{3} \cdot 3^{x})

Take the constant out:

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

= 0.9 \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}

= 0.9 (\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)

= 0.9 (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}

= 0.9 (3^{1 + x} x^{2} + ln (3) \cdot 3^{x} x^{3})

What is the derivative of 0.9x^33^x ?
The derivative of 0.9x^33^x is 0.9(3^{1+x}x^2+ln(3)*3^xx^3)
What is the first derivative of 0.9x^33^x ?
The first derivative of 0.9x^33^x is 0.9(3^{1+x}x^2+ln(3)*3^xx^3)