What is the derivative of (1+x^2)log_{2}(x) ?

The derivative of (1+x^2)log_{2}(x) is (1+x^2+2x^2ln(x))/(ln(2)x)

What is the first derivative of (1+x^2)log_{2}(x) ?

The first derivative of (1+x^2)log_{2}(x) is (1+x^2+2x^2ln(x))/(ln(2)x)

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derivative of

(1 + x^{2}) lo g_{2} (x)

\frac{1 + x ^{2} + 2 x ^{2} ln ( x )}{ln ( 2 ) x}

Solution steps

\frac{d}{d x} ((1 + x^{2}) lo g_{2} (x))

Apply the Product Rule:

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

f = 1 + x^{2}, g = lo g_{2} (x)

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

\frac{d}{d x} (1 + x^{2}) = 2 x

\frac{d}{d x} (lo g_{2} (x)) = \frac{1}{x ln ( 2 )}

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

Simplify

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

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

What is the derivative of (1+x^2)log_{2}(x) ?
The derivative of (1+x^2)log_{2}(x) is (1+x^2+2x^2ln(x))/(ln(2)x)
What is the first derivative of (1+x^2)log_{2}(x) ?
The first derivative of (1+x^2)log_{2}(x) is (1+x^2+2x^2ln(x))/(ln(2)x)