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Use implicit differentiation to find an equation of the tangent line to the curve

sin(x+y)=4x-4y
at the point
(pi,pi).
Tangent Line Equation:

Use implicit differentiation to find an equation of the tangent line to the curve $\newline$ $\sin (x+y)=4 x-4 y$ $\newline$ at the point $(\pi, \pi)$ . $\newline$ Tangent Line Equation:

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Find equations of tangent lines using limits

Full solution

Q. Use implicit differentiation to find an equation of the tangent line to the curve

\newline

\sin (x+y)=4 x-4 y

\newline

at the point

(\pi, \pi)

.

\newline

Tangent Line Equation:

Differentiate with respect to $x$ : Step $1$ : Differentiate both sides of the equation $\sin(x+y) = 4x - 4y$ with respect to $x$ using implicit differentiation.
Set derivatives equal and solve: Step $2$ : Set the derivatives equal to each other and solve for $\frac{dy}{dx}$ .
Evaluate at point $\pi, \pi$ : Step $3$ : Evaluate $\frac{dy}{dx}$ at the point $\pi, \pi$ .
Find tangent line using point-slope form: Step $4$ : Use the point-slope form of the equation of a line to find the tangent line at $(\pi, \pi)$ .

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