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Popular >

implicit (dy)/(dx),9cos(xy)=4x+5y

Solution

implicit derivative

\frac{d y}{d x}, 9 cos (x y) = 4 x + 5 y

Solution

\frac{d y}{d x} = - \frac{4 + 9 y sin ( x y )}{5 + 9 x sin ( x y )}

Solution steps

9 cos (x y) = 4 x + 5 y

Treat

y

as

y (x)

Differentiate both sides:

- 9 sin (x y) (y + x \frac{d y}{d x}) = 4 + 5 \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{4 + 9 y sin ( x y )}{5 + 9 x sin ( x y )}

\frac{d y}{d x} = - \frac{4 + 9 y sin ( x y )}{5 + 9 x sin ( x y )}

Popular Examples

integral from-2 to 2 of y^2-2-y

\int_{- 2}^{2} y^{2} - 2 - y d y

integral of (5-50x)/(sqrt(36-25x^2))

\int \frac{5 - 50 x}{36 - 25 x ^{2}} d x

integral of (x^2)/2-2x

\int \frac{x ^{2}}{2} - 2 x d x

integral of 1/((x+1)(3x+1))

\int \frac{1}{( x + 1 ) ( 3 x + 1 )} d x

integral of x/(sqrt(5+x-x^2))

\int \frac{x}{5 + x - x ^{2}} d x

Frequently Asked Questions (FAQ)

What is implicit (dy)/(dx),9cos(xy)=4x+5y ?
The answer to implicit (dy)/(dx),9cos(xy)=4x+5y is (dy)/(dx)=-(4+9ysin(xy))/(5+9xsin(xy))