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Popular >

derivative of x+y*ln(5-x/2)

Solution

\frac{d}{d x} (x + y \cdot ln (5 - \frac{x}{2}))

Solution

1 + ln (5 - \frac{x}{2}) \frac{d y}{d x} - \frac{y}{10 - x}

Solution steps

\frac{d}{d x} (x + y ln (5 - \frac{x}{2}))

Apply the Sum/Difference Rule:

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

= \frac{d x}{d x} + \frac{d}{d x} (y ln (5 - \frac{x}{2}))

\frac{d x}{d x} = 1

\frac{d}{d x} (y ln (5 - \frac{x}{2})) = ln (5 - \frac{x}{2}) \frac{d y}{d x} - \frac{y}{10 - x}

= 1 + ln (5 - \frac{x}{2}) \frac{d y}{d x} - \frac{y}{10 - x}

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Frequently Asked Questions (FAQ)

What is the derivative of x+y*ln(5-x/2) ?
The derivative of x+y*ln(5-x/2) is 1+ln(5-x/2)(dy)/(dx)-y/(10-x)
What is the first derivative of x+y*ln(5-x/2) ?
The first derivative of x+y*ln(5-x/2) is 1+ln(5-x/2)(dy)/(dx)-y/(10-x)