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arlik [135]
2 years ago
7

If ln(4x+y)=2x-3,then dy/dx=

Mathematics
1 answer:
Viktor [21]2 years ago
4 0

\ln(4x+y)=2x-3

Differentiate both sides wrt x:

\dfrac{\mathrm d(\ln(4x+y))}{\mathrm dx}=\dfrac{\mathrm d(2x-3)}{\mathrm dx}

By the chain rule, we get

\dfrac1{4x+y}\dfrac{\mathrm d(4x+y)}{\mathrm dx}=2

\dfrac{4+\frac{\mathrm dy}{\mathrm dx}}{4x+y}=2

Solve for \frac{\mathrm dy}{\mathrm dx}:

4+\dfrac{\mathrm dy}{\mathrm dx}=8x+2y

\boxed{\dfrac{\mathrm dy}{\mathrm dx}=8x+2y-4}

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\huge\text{Hey there!}

\large\text{Just SIMPLIFY the given EQUATION or find the DIFFERENCE}\\\large\text{OF the SQUARES... Here is the formula: }\mathsf{\bf a^2 - b^2 =(a+b)(a-b)}

\large\text{Equation: }\mathsf{\dfrac{(4x^2-9)}{(2x + 3)}}

\large\text{Rewrite }\mathsf{ 4x^9 - 9}\large\text{ in the formation of }\mathsf{a^2 - b^2}\large\text{ whereas}\mathsf{a = 2x \ \&\ b = 3.}

\large\text{Equation: }\mathsf{\dfrac{(2x)^2-3^2}{2x + 3}}

\large\text{This is where you try to do the DIFFERENCE OF its SQUARES}

\mathsf{\dfrac{(2x + 3)(2x - 3)}{2x + 3}}

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\large\text{This leaves us with }\mathsf{\bf 2x - 3}\large\text{ as your POSSIBLE  ANSWER}

\boxed{\boxed{\large\text{Answer: \huge \bf 2x - 3}}}\huge\checkmark

\text{Good luck on your assignment and enjoy your day!}

~\frak{Amphitrite1040:)}

\large\text{Note: There is/are many ways to solve for equations like this.... this was just}\\\large\text{the quickest and easiest way to understand it!}

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