What is the derivative of y=x^5log_{2}(x) ?

The derivative of y=x^5log_{2}(x) is (x^4+5x^4ln(x))/(ln(2))

What is the first derivative of y=x^5log_{2}(x) ?

The first derivative of y=x^5log_{2}(x) is (x^4+5x^4ln(x))/(ln(2))

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derivative of

y = x^{5} lo g_{2} (x)

\frac{x ^{4} + 5 x ^{4} ln ( x )}{ln ( 2 )}

Solution steps

\frac{d}{d x} (x^{5} lo g_{2} (x))

Apply the Product Rule:

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

f = x^{5}, g = lo g_{2} (x)

= \frac{d}{d x} (x^{5}) lo g_{2} (x) + \frac{d}{d x} (lo g_{2} (x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} lo g_{2} (x) + \frac{1}{x ln ( 2 )} x^{5}

Simplify

5 x^{4} lo g_{2} (x) + \frac{1}{x ln ( 2 )} x^{5} : \frac{x ^{4} + 5 x ^{4} ln ( x )}{ln ( 2 )}

= \frac{x ^{4} + 5 x ^{4} ln ( x )}{ln ( 2 )}

d er i v a t i v e f (x) = e^{2 x - 3}

d er i v a t i v e sin (5 x^{2} - 3 x + 4)

d er i v a t i v e y = 63

d er i v a t i v e y = sin^{2} (3 x + 4)

d er i v a t i v e 3 x - 2 y = lo g_{10} (3 x + 2 y)

What is the derivative of y=x^5log_{2}(x) ?
The derivative of y=x^5log_{2}(x) is (x^4+5x^4ln(x))/(ln(2))
What is the first derivative of y=x^5log_{2}(x) ?
The first derivative of y=x^5log_{2}(x) is (x^4+5x^4ln(x))/(ln(2))