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Popular >

derivative of nlog_{10}(n)

Solution

derivative of

n lo g_{10} (n)

Solution

lo g_{10} (n) + \frac{1}{ln ( 10 )}

Solution steps

\frac{d}{d n} (n lo g_{10} (n))

Apply the Product Rule:

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

f = n, g = lo g_{10} (n)

= \frac{d n}{d n} lo g_{10} (n) + \frac{d}{d n} (lo g_{10} (n)) n

\frac{d n}{d n} = 1

\frac{d}{d n} (lo g_{10} (n)) = \frac{1}{n ln ( 10 )}

= 1 \cdot lo g_{10} (n) + \frac{1}{n ln ( 10 )} n

Simplify

1 \cdot lo g_{10} (n) + \frac{1}{n ln ( 10 )} n : lo g_{10} (n) + \frac{1}{ln ( 10 )}

= lo g_{10} (n) + \frac{1}{ln ( 10 )}

Popular Examples

integral of 1/((x-1)^{2/3)}

\int \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x

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\int 9 x^{2} sin (8 x) d x

(\partial)/(\partial y)(sqrt(tan(x)+y))

\frac{\partial}{\partial y} (tan (x) + y)

derivative of 3+3sin(x)

\frac{d}{d x} (3 + 3 sin (x))

limit as x approaches 5 of xsqrt(34-x^2)

x \to 5 lim (x 34 - x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of nlog_{10}(n) ?
The derivative of nlog_{10}(n) is log_{10}(n)+1/(ln(10))
What is the first derivative of nlog_{10}(n) ?
The first derivative of nlog_{10}(n) is log_{10}(n)+1/(ln(10))