What is the derivative of x^{1/2}log_{10}(x) ?

The derivative of x^{1/2}log_{10}(x) is (log_{10}(x))/(2x^{1/2)}+1/(ln(10)x^{1/2)}

What is the first derivative of x^{1/2}log_{10}(x) ?

The first derivative of x^{1/2}log_{10}(x) is (log_{10}(x))/(2x^{1/2)}+1/(ln(10)x^{1/2)}

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derivative of

x^{\frac{1}{2}} lo g_{10} (x)

\frac{lo g _{10} ( x )}{2 x ^{\frac{1}{2}}} + \frac{1}{ln ( 10 ) x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (x^{\frac{1}{2}} lo g_{10} (x))

Apply the Product Rule:

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

f = x^{\frac{1}{2}}, g = lo g_{10} (x)

= \frac{d}{d x} (x^{\frac{1}{2}}) lo g_{10} (x) + \frac{d}{d x} (lo g_{10} (x)) x^{\frac{1}{2}}

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

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

= \frac{1}{2 x ^{\frac{1}{2}}} lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{\frac{1}{2}}

Simplify

\frac{1}{2 x ^{\frac{1}{2}}} lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{\frac{1}{2}} : \frac{lo g _{10} ( x )}{2 x ^{\frac{1}{2}}} + \frac{1}{ln ( 10 ) x ^{\frac{1}{2}}}

= \frac{lo g _{10} ( x )}{2 x ^{\frac{1}{2}}} + \frac{1}{ln ( 10 ) x ^{\frac{1}{2}}}

What is the derivative of x^{1/2}log_{10}(x) ?
The derivative of x^{1/2}log_{10}(x) is (log_{10}(x))/(2x^{1/2)}+1/(ln(10)x^{1/2)}
What is the first derivative of x^{1/2}log_{10}(x) ?
The first derivative of x^{1/2}log_{10}(x) is (log_{10}(x))/(2x^{1/2)}+1/(ln(10)x^{1/2)}