What is the derivative of y=x6^x ?

The derivative of y=x6^x is 6^x+ln(6)*6^xx

What is the first derivative of y=x6^x ?

The first derivative of y=x6^x is 6^x+ln(6)*6^xx

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derivative of

y = x 6^{x}

6^{x} + ln (6) \cdot 6^{x} x

Solution steps

\frac{d}{d x} (x \cdot 6^{x})

Apply the Product Rule:

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

f = x, g = 6^{x}

= \frac{d x}{d x} 6^{x} + \frac{d}{d x} (6^{x}) x

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

\frac{d}{d x} (6^{x}) = 6^{x} ln (6)

= 1 \cdot 6^{x} + 6^{x} ln (6) x

Simplify

= 6^{x} + ln (6) \cdot 6^{x} x

x (x + y) (\frac{d y}{d x}) + y (3 x + y) = 0

y = ln (arctan (4 x))

\int_{1}^{3} 5 r^{3} ln (r) d r

y^{^{''}} - y^{^{'}} - 2 y = 2 e^{- t}

\int tan^{3} (x) sec^{\frac{1}{2}} (x) d x

What is the derivative of y=x6^x ?
The derivative of y=x6^x is 6^x+ln(6)*6^xx
What is the first derivative of y=x6^x ?
The first derivative of y=x6^x is 6^x+ln(6)*6^xx