What is the derivative of 3^xlog_{3}(x) ?

The derivative of 3^xlog_{3}(x) is 3^xln(x)+(3^x)/(ln(3)x)

What is the first derivative of 3^xlog_{3}(x) ?

The first derivative of 3^xlog_{3}(x) is 3^xln(x)+(3^x)/(ln(3)x)

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derivative of

3^{x} lo g_{3} (x)

3^{x} ln (x) + \frac{3 ^{x}}{ln ( 3 ) x}

Solution steps

\frac{d}{d x} (3^{x} lo g_{3} (x))

Apply the Product Rule:

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

f = 3^{x}, g = lo g_{3} (x)

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

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

\frac{d}{d x} (lo g_{3} (x)) = \frac{1}{x ln ( 3 )}

= 3^{x} ln (3) lo g_{3} (x) + \frac{1}{x ln ( 3 )} \cdot 3^{x}

Simplify

3^{x} ln (3) lo g_{3} (x) + \frac{1}{x ln ( 3 )} \cdot 3^{x} : 3^{x} ln (x) + \frac{3 ^{x}}{ln ( 3 ) x}

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

a re a 9 - x^{2}, - 8 x

\frac{d}{d x} (\frac{x}{x + 5})

\frac{d y}{d x} = x (4 - y)

n = 0 \sum \infty n (\frac{3}{5})^{n}

25 x^{2} y^{^{''}} + 25 x y^{^{'}} + y = 0

What is the derivative of 3^xlog_{3}(x) ?
The derivative of 3^xlog_{3}(x) is 3^xln(x)+(3^x)/(ln(3)x)
What is the first derivative of 3^xlog_{3}(x) ?
The first derivative of 3^xlog_{3}(x) is 3^xln(x)+(3^x)/(ln(3)x)