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 )}

\int_{0}^{1} (x^{13} + 1 3^{x}) d x

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

\int \frac{arctan ^{5} ( x )}{1 + x ^{2}} d x

\frac{d y}{d x}, 9 x = y^{2}

x \to 0 + lim ((1 + 4 x)^{\frac{3}{x}})

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))