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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

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

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

= 3 (2 x lo g_{3} (x) + \frac{1}{x ln ( 3 )} x^{2})

Simplify

3 (2 x lo g_{3} (x) + \frac{1}{x ln ( 3 )} x^{2}) : \frac{3 ( x + 2 x ln ( x ) )}{ln ( 3 )}

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

k \to 0 lim (\frac{x ^{2} k + 3 x k ^{2} + k ^{2}}{2 x k + 5 k ^{2}})

\int sin^{7} (\frac{x}{9}) cos (\frac{x}{9}) d x

\int ln (3 x + 1) d x

f (x) = x^{3} - 7 x^{2}

\frac{d y}{d x} = (e^{x} + 10)^{2}

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