What is the derivative of log_{10}(x^2+y^2) ?

The derivative of log_{10}(x^2+y^2) is (2x+2y\frac{dy)/(dx)}{ln(10)(x^2+y^2)}

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

The first derivative of log_{10}(x^2+y^2) is (2x+2y\frac{dy)/(dx)}{ln(10)(x^2+y^2)}

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

\frac{2 x + 2 y \frac{d y}{d x}}{ln ( 10 ) ( x ^{2} + y ^{2} )}

Solution steps

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

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( x ^{2} + y ^{2} )}{ln ( 10 )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{2} + y^{2}))

Apply the chain rule:

\frac{1}{x ^{2} + y ^{2}} \frac{d}{d x} (x^{2} + y^{2})

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

\frac{d}{d x} (x^{2} + y^{2}) = 2 x + 2 y \frac{d y}{d x}

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} + y ^{2}} (2 x + 2 y \frac{d y}{d x})

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} + y ^{2}} (2 x + 2 y \frac{d y}{d x}) : \frac{2 x + 2 y \frac{d y}{d x}}{ln ( 10 ) ( x ^{2} + y ^{2} )}

= \frac{2 x + 2 y \frac{d y}{d x}}{ln ( 10 ) ( x ^{2} + y ^{2} )}

a^{2} + x^{2}

\frac{d}{d x} (\frac{2 \cdot k}{x + d})

y = 3 sin (3 x + 7)

4 x^{3} - 9 x^{2} + 28 x - 68

\frac{y}{( 3 y ^{2} - x )}

What is the derivative of log_{10}(x^2+y^2) ?
The derivative of log_{10}(x^2+y^2) is (2x+2y\frac{dy)/(dx)}{ln(10)(x^2+y^2)}
What is the first derivative of log_{10}(x^2+y^2) ?
The first derivative of log_{10}(x^2+y^2) is (2x+2y\frac{dy)/(dx)}{ln(10)(x^2+y^2)}