What is the derivative of y=x5^{x+4} ?

The derivative of y=x5^{x+4} is 5^{x+4}+ln(5)*5^{x+4}x

What is the first derivative of y=x5^{x+4} ?

The first derivative of y=x5^{x+4} is 5^{x+4}+ln(5)*5^{x+4}x

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derivative of

y = x 5^{x + 4}

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

Solution steps

\frac{d}{d x} (x \cdot 5^{x + 4})

Apply the Product Rule:

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

f = x, g = 5^{x + 4}

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

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

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

= 1 \cdot 5^{x + 4} + ln (5) \cdot 5^{x + 4} x

Simplify

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

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What is the derivative of y=x5^{x+4} ?
The derivative of y=x5^{x+4} is 5^{x+4}+ln(5)*5^{x+4}x
What is the first derivative of y=x5^{x+4} ?
The first derivative of y=x5^{x+4} is 5^{x+4}+ln(5)*5^{x+4}x