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Popular >

implicit (dy)/(dx),5cos(8x)sin(5y)=8

Solution

implicit derivative

\frac{d y}{d x}, 5 cos (8 x) sin (5 y) = 8

Solution

\frac{d y}{d x} = \frac{8 sin ( 5 y ) sin ( 8 x )}{5 cos ( 5 y ) cos ( 8 x )}

Solution steps

5 cos (8 x) sin (5 y) = 8

Treat

y

as

y (x)

Differentiate both sides:

5 (- 8 sin (5 y) sin (8 x) + 5 cos (5 y) cos (8 x) \frac{d y}{d x}) = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{8 sin ( 5 y ) sin ( 8 x )}{5 cos ( 5 y ) cos ( 8 x )}

\frac{d y}{d x} = \frac{8 sin ( 5 y ) sin ( 8 x )}{5 cos ( 5 y ) cos ( 8 x )}

Popular Examples

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y^'=0.0011y*(2900-y)

y^{^{'}} = 0.0011 y \cdot (2900 - y)

integral of 8e^{5x+e^{5x}}

\int 8 e^{5 x + e^{5 x}} d x

integral of cot^2(x)csc^6(x)

\int cot^{2} (x) csc^{6} (x) d x

Frequently Asked Questions (FAQ)

What is implicit (dy)/(dx),5cos(8x)sin(5y)=8 ?
The answer to implicit (dy)/(dx),5cos(8x)sin(5y)=8 is (dy)/(dx)=(8sin(5y)sin(8x))/(5cos(5y)cos(8x))