What is implicit (dp)/(dx),x^2+3px+p^2=79 ?

The answer to implicit (dp)/(dx),x^2+3px+p^2=79 is (dp)/(dx)=(-2x-3p)/(3x+2p)

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implicit (dp)/(dx),x^2+3px+p^2=79

implicit derivative

\frac{d p}{d x}, x^{2} + 3 p x + p^{2} = 79

\frac{d p}{d x} = \frac{- 2 x - 3 p}{3 x + 2 p}

Solution steps

x^{2} + 3 p x + p^{2} = 79

Treat

p

p (x)

Differentiate both sides:

2 x + 3 (x \frac{d p}{d x} + p) + 2 p \frac{d p}{d x} = 0

Isolate

\frac{d p}{d x} : \frac{d p}{d x} = \frac{- 2 x - 3 p}{3 x + 2 p}

\frac{d p}{d x} = \frac{- 2 x - 3 p}{3 x + 2 p}

\frac{d}{d x} (- \frac{9}{( x + 1 ) ^{2}} + 1)

\int p (p + 9)^{6} d p

f (x) = \frac{1}{3} (5 - x)^{4}

y^{^{''}} - 6 y^{^{'}} + 8 y = e^{x} (11 - 6 x)

\frac{3 s + 5}{s ^{2} + 4 s + 13}

What is implicit (dp)/(dx),x^2+3px+p^2=79 ?
The answer to implicit (dp)/(dx),x^2+3px+p^2=79 is (dp)/(dx)=(-2x-3p)/(3x+2p)