What is the derivative of y=x^53^x ?

The derivative of y=x^53^x is 5x^4*3^x+3^xln(3)x^5

What is the first derivative of y=x^53^x ?

The first derivative of y=x^53^x is 5x^4*3^x+3^xln(3)x^5

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derivative of

y = x^{5} 3^{x}

5 x^{4} \cdot 3^{x} + 3^{x} ln (3) x^{5}

Solution steps

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

Apply the Product Rule:

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

f = x^{5}, g = 3^{x}

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} \cdot 3^{x} + 3^{x} ln (3) x^{5}

What is the derivative of y=x^53^x ?
The derivative of y=x^53^x is 5x^4*3^x+3^xln(3)x^5
What is the first derivative of y=x^53^x ?
The first derivative of y=x^53^x is 5x^4*3^x+3^xln(3)x^5