What is the derivative of 2log_{10}(x-3sqrt(x)) ?

The derivative of 2log_{10}(x-3sqrt(x)) is (4-3ln(10)sqrt(x))/(2ln(10)x)

What is the first derivative of 2log_{10}(x-3sqrt(x)) ?

The first derivative of 2log_{10}(x-3sqrt(x)) is (4-3ln(10)sqrt(x))/(2ln(10)x)

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\frac{d}{d x} (2 lo g_{10} (x) - 3 x)

\frac{4 - 3 ln ( 10 ) x}{2 ln ( 10 ) x}

Solution steps

\frac{d}{d x} (2 lo g_{10} (x) - 3 x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 lo g_{10} (x)) - \frac{d}{d x} (3 x)

\frac{d}{d x} (2 lo g_{10} (x)) = \frac{2}{ln ( 10 ) x}

\frac{d}{d x} (3 x) = \frac{3}{2 x}

= \frac{2}{ln ( 10 ) x} - \frac{3}{2 x}

Simplify

\frac{2}{ln ( 10 ) x} - \frac{3}{2 x} : \frac{4 - 3 ln ( 10 ) x}{2 ln ( 10 ) x}

= \frac{4 - 3 ln ( 10 ) x}{2 ln ( 10 ) x}

\int \frac{2 x ^{2}}{4 x - x ^{2}} d x

\frac{3 x + 4}{3 x - 4}

\int sec^{5} (x) - sec^{3} (x) d x

x (y + 1) d x + y (x - 1) d y = 0

x \to 0 lim (\frac{x}{x ^{2} - 1})

What is the derivative of 2log_{10}(x-3sqrt(x)) ?
The derivative of 2log_{10}(x-3sqrt(x)) is (4-3ln(10)sqrt(x))/(2ln(10)x)
What is the first derivative of 2log_{10}(x-3sqrt(x)) ?
The first derivative of 2log_{10}(x-3sqrt(x)) is (4-3ln(10)sqrt(x))/(2ln(10)x)