What is the derivative of x^2log_{3}(x^3) ?

The derivative of x^2log_{3}(x^3) is (3x+2xln(x^3))/(ln(3))

What is the first derivative of x^2log_{3}(x^3) ?

The first derivative of x^2log_{3}(x^3) is (3x+2xln(x^3))/(ln(3))

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derivative of

x^{2} lo g_{3} (x^{3})

\frac{3 x + 2 x ln ( x ^{3} )}{ln ( 3 )}

Solution steps

\frac{d}{d x} (x^{2} lo g_{3} (x^{3}))

Apply the Product Rule:

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

f = x^{2}, g = lo g_{3} (x^{3})

= \frac{d}{d x} (x^{2}) lo g_{3} (x^{3}) + \frac{d}{d x} (lo g_{3} (x^{3})) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 x lo g_{3} (x^{3}) + \frac{3}{ln ( 3 ) x} x^{2}

Simplify

2 x lo g_{3} (x^{3}) + \frac{3}{ln ( 3 ) x} x^{2} : \frac{3 x + 2 x ln ( x ^{3} )}{ln ( 3 )}

= \frac{3 x + 2 x ln ( x ^{3} )}{ln ( 3 )}

\int (8 x - \frac{7}{x}) d x

y = cos (x), at x = \frac{3 π}{2}

f (x) = \frac{5}{( 2 x - 3 ) ^{4}}

\frac{d}{d x} (sin (x) ln (5 x))

e^{19}

What is the derivative of x^2log_{3}(x^3) ?
The derivative of x^2log_{3}(x^3) is (3x+2xln(x^3))/(ln(3))
What is the first derivative of x^2log_{3}(x^3) ?
The first derivative of x^2log_{3}(x^3) is (3x+2xln(x^3))/(ln(3))