What is implicit (dy)/(dx),e^{9x}=sin(x+8y) ?

The answer to implicit (dy)/(dx),e^{9x}=sin(x+8y) is (dy)/(dx)=(9e^{9x}-cos(x+8y))/(8cos(x+8y))

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implicit (dy)/(dx),e^{9x}=sin(x+8y)

implicit derivative

\frac{d y}{d x}, e^{9 x} = sin (x + 8 y)

\frac{d y}{d x} = \frac{9 e ^{9 x} - cos ( x + 8 y )}{8 cos ( x + 8 y )}

Solution steps

e^{9 x} = sin (x + 8 y)

Treat

y

y (x)

Differentiate both sides:

e^{9 x} \cdot 9 = cos (x + 8 y) (1 + 8 \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{9 e ^{9 x} - cos ( x + 8 y )}{8 cos ( x + 8 y )}

\frac{d y}{d x} = \frac{9 e ^{9 x} - cos ( x + 8 y )}{8 cos ( x + 8 y )}

x \to 8 - lim (\frac{∣ x - 8 ∣}{x - 8})

im pl i c i t \frac{d y}{d x}, 9 x = y^{2}

\int x \cdot e^{3 \cdot x} d x

x \to - 3 lim (5 (3 x^{2} - 24 x + 3))

d er i v a t i v e 2 4 9 - x^{2}

What is implicit (dy)/(dx),e^{9x}=sin(x+8y) ?
The answer to implicit (dy)/(dx),e^{9x}=sin(x+8y) is (dy)/(dx)=(9e^{9x}-cos(x+8y))/(8cos(x+8y))