What is implicit (dy)/(dx),y*cos(x)=2x^2+5y^2 ?

The answer to implicit (dy)/(dx),y*cos(x)=2x^2+5y^2 is (dy)/(dx)=(4x+ysin(x))/(cos(x)-10y)

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implicit (dy)/(dx),y*cos(x)=2x^2+5y^2

implicit derivative

\frac{d y}{d x}, y \cdot cos (x) = 2 x^{2} + 5 y^{2}

\frac{d y}{d x} = \frac{4 x + y sin ( x )}{cos ( x ) - 10 y}

Solution steps

y cos (x) = 2 x^{2} + 5 y^{2}

Treat

y

y (x)

Differentiate both sides:

cos (x) \frac{d y}{d x} - sin (x) y = 4 x + 10 y \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{4 x + y sin ( x )}{cos ( x ) - 10 y}

\frac{d y}{d x} = \frac{4 x + y sin ( x )}{cos ( x ) - 10 y}

\int_{5}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

\int_{\frac{1}{7}}^{5} 14 x ln (7 x) d x

f (x) = (x + 1) (x^{3} + x - 2)

\int_{1}^{4} \frac{x ^{2} + 6}{5 x - x ^{2}} d x

\int cos^{2} (π) x d x

What is implicit (dy)/(dx),y*cos(x)=2x^2+5y^2 ?
The answer to implicit (dy)/(dx),y*cos(x)=2x^2+5y^2 is (dy)/(dx)=(4x+ysin(x))/(cos(x)-10y)