What is the derivative of x^2log_{2}(7-6x) ?

The derivative of x^2log_{2}(7-6x) is (-6x^2+2xln(7-6x)(7-6x))/(ln(2)(7-6x))

What is the first derivative of x^2log_{2}(7-6x) ?

The first derivative of x^2log_{2}(7-6x) is (-6x^2+2xln(7-6x)(7-6x))/(ln(2)(7-6x))

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\frac{d}{d x} (x^{2} lo g_{2} (7 - 6 x))

\frac{- 6 x ^{2} + 2 x ln ( 7 - 6 x ) ( 7 - 6 x )}{ln ( 2 ) ( 7 - 6 x )}

Solution steps

\frac{d}{d x} (x^{2} lo g_{2} (7 - 6 x))

Apply the Product Rule:

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

f = x^{2}, g = lo g_{2} (7 - 6 x)

= \frac{d}{d x} (x^{2}) lo g_{2} (7 - 6 x) + \frac{d}{d x} (lo g_{2} (7 - 6 x)) x^{2}

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

\frac{d}{d x} (lo g_{2} (7 - 6 x)) = - \frac{6}{ln ( 2 ) ( 7 - 6 x )}

= 2 x lo g_{2} (7 - 6 x) + (- \frac{6}{ln ( 2 ) ( 7 - 6 x )}) x^{2}

Simplify

2 x lo g_{2} (7 - 6 x) + (- \frac{6}{ln ( 2 ) ( 7 - 6 x )}) x^{2} : \frac{- 6 x ^{2} + 2 x ln ( 7 - 6 x ) ( 7 - 6 x )}{ln ( 2 ) ( 7 - 6 x )}

= \frac{- 6 x ^{2} + 2 x ln ( 7 - 6 x ) ( 7 - 6 x )}{ln ( 2 ) ( 7 - 6 x )}

\int 6 sin^{2} (3 x) cos (3 x) ln (sin (3 x)) d x

\int_{0}^{4} 4 x - 2 x d x

\frac{d y}{d x} = e^{3 x} + 9 y

x \to - 2 lim (\frac{sin ( - π x )}{2 + x})

\int_{2}^{3} \frac{22}{3 - x} d x

What is the derivative of x^2log_{2}(7-6x) ?
The derivative of x^2log_{2}(7-6x) is (-6x^2+2xln(7-6x)(7-6x))/(ln(2)(7-6x))
What is the first derivative of x^2log_{2}(7-6x) ?
The first derivative of x^2log_{2}(7-6x) is (-6x^2+2xln(7-6x)(7-6x))/(ln(2)(7-6x))