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

The derivative of x^2log_{2}(x^3) is (3x+6xln(x))/(ln(2))

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

The first derivative of x^2log_{2}(x^3) is (3x+6xln(x))/(ln(2))

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

\frac{3 x + 6 x ln ( x )}{ln ( 2 )}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x lo g_{2} (x^{3}) + \frac{3}{ln ( 2 ) x} x^{2} : \frac{3 x + 6 x ln ( x )}{ln ( 2 )}

= \frac{3 x + 6 x ln ( x )}{ln ( 2 )}

u^{5}

\frac{d}{d x} (\frac{x ^{4}}{3} - 7 x)

e^{- 2 t}

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

n = 1 \sum \infty \frac{( - 1 )}{n}

What is the derivative of x^2log_{2}(x^3) ?
The derivative of x^2log_{2}(x^3) is (3x+6xln(x))/(ln(2))
What is the first derivative of x^2log_{2}(x^3) ?
The first derivative of x^2log_{2}(x^3) is (3x+6xln(x))/(ln(2))