What is implicit (dy)/(dx),e^{4x}=sin(x+5y) ?

The answer to implicit (dy)/(dx),e^{4x}=sin(x+5y) is (dy)/(dx)=(4e^{4x}-cos(x+5y))/(5cos(x+5y))

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implicit (dy)/(dx),e^{4x}=sin(x+5y)

implicit derivative

\frac{d y}{d x}, e^{4 x} = sin (x + 5 y)

\frac{d y}{d x} = \frac{4 e ^{4 x} - cos ( x + 5 y )}{5 cos ( x + 5 y )}

Solution steps

e^{4 x} = sin (x + 5 y)

Treat

y

y (x)

Differentiate both sides:

e^{4 x} \cdot 4 = cos (x + 5 y) (1 + 5 \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{4 e ^{4 x} - cos ( x + 5 y )}{5 cos ( x + 5 y )}

\frac{d y}{d x} = \frac{4 e ^{4 x} - cos ( x + 5 y )}{5 cos ( x + 5 y )}

\frac{e ^{x}}{1 + x}

y^{^{''}} - 4 y^{^{'}} + 6 y = e^{3 x} - 21

\int \frac{sin ( x )}{1 + cos ^{2} ( x )} d x

\int (e^{- x} - e^{3}) (e^{x} + e^{- 5}) d x

p^{^{'}}

What is implicit (dy)/(dx),e^{4x}=sin(x+5y) ?
The answer to implicit (dy)/(dx),e^{4x}=sin(x+5y) is (dy)/(dx)=(4e^{4x}-cos(x+5y))/(5cos(x+5y))