What is the derivative of 1+xln(xy-5) ?

The derivative of 1+xln(xy-5) is (x(x\frac{dy)/(dx)+y)}{xy-5}+ln(xy-5)

What is the first derivative of 1+xln(xy-5) ?

The first derivative of 1+xln(xy-5) is (x(x\frac{dy)/(dx)+y)}{xy-5}+ln(xy-5)

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\frac{d}{d x} (1 + x ln (x y - 5))

\frac{x ( x \frac{d y}{d x} + y )}{x y - 5} + ln (x y - 5)

Solution steps

\frac{d}{d x} (1 + x ln (x y - 5))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (1) + \frac{d}{d x} (x ln (x y - 5))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (x ln (x y - 5)) = ln (x y - 5) + \frac{x ( x \frac{d y}{d x} + y )}{x y - 5}

= 0 + ln (x y - 5) + \frac{x ( x \frac{d y}{d x} + y )}{x y - 5}

Simplify

= \frac{x ( x \frac{d y}{d x} + y )}{x y - 5} + ln (x y - 5)

y^{^{'''}} + y^{^{'}} = 0

x \to 2 lim (3 x^{2} + 2 x - 1)

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

\int \frac{y ^{4} + y ^{2} - 1}{y ^{3} + y} d y

n = 0 \sum \infty \frac{5}{2 ^{n}}

What is the derivative of 1+xln(xy-5) ?
The derivative of 1+xln(xy-5) is (x(x\frac{dy)/(dx)+y)}{xy-5}+ln(xy-5)
What is the first derivative of 1+xln(xy-5) ?
The first derivative of 1+xln(xy-5) is (x(x\frac{dy)/(dx)+y)}{xy-5}+ln(xy-5)