What is (\partial)/(\partial x)(x+3log_{10}(x)-y^2) ?

The answer to (\partial)/(\partial x)(x+3log_{10}(x)-y^2) is 3/(ln(10)x)+1

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(\partial)/(\partial x)(x+3log_{10}(x)-y^2)

\frac{\partial}{\partial x} (x + 3 lo g_{10} (x) - y^{2})

\frac{3}{ln ( 10 ) x} + 1

Solution steps

\frac{\partial}{\partial x} (x + 3 lo g_{10} (x) - y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (3 lo g_{10} (x)) - \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (3 lo g_{10} (x)) = \frac{3}{ln ( 10 ) x}

\frac{\partial}{\partial x} (y^{2}) = 0

= 1 + \frac{3}{ln ( 10 ) x} - 0

Simplify

= \frac{3}{ln ( 10 ) x} + 1

\int \frac{18}{x 1 + 2 x} d x

x \to 1 + lim (\frac{x + 1}{x - 1})

y^{^{''}} - 5 y^{^{'}} + 4 y = 0

\int \frac{6 x}{x ^{2} + 1} d x

\frac{d ^{2}}{d x ^{2}} ((6 x^{2} + 8)^{6})

What is (\partial)/(\partial x)(x+3log_{10}(x)-y^2) ?
The answer to (\partial)/(\partial x)(x+3log_{10}(x)-y^2) is 3/(ln(10)x)+1