Solve the equation. (dy)/(dx)=(4x^(3))/(cos(y)) Choose 1 answer: (A) y=arccos(4x^(3))+C (B) y=arccos(4x^(3)+C) (C) y=arcsin(x^(4)+C) (D) y=arcsin(x^(4))+C

Separate variables x and y: To solve the differential equation (dy)/(dx)=(4x^(3))/(cos(y)), we need to separate the variables x and y. This means we want to get all the y terms on one side of the equation and all the x terms on the other side.Multiply by cos(y): We multiply both sides by cos(y) to get cos(y) dy = 4x^3 dx.Integrate both sides: Now we integrate both sides of the equation. The left side with respect to y and the right side with respect to x.Apply inverse sine: The integral of cos(y) dy is sin(y), and the integral of 4x^3 dx is x^4. So we have sin(y) = x^4 + C, where C is the constant of integration.Final solution: To solve for y, we take the inverse sine (arcsin) of both sides. y = arcsin(x^4 + C)Looking at the answer choices, we see that option (C) y=arcsin(x^(4)+C) matches our solution.

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Solve the equation.

(dy)/(dx)=(4x^(3))/(cos(y))
Choose 1 answer:
(A)
y=arccos(4x^(3))+C
(B)
y=arccos(4x^(3)+C)
(C)
y=arcsin(x^(4)+C)
(D)
y=arcsin(x^(4))+C

Solve the equation. $\newline$ $\frac{d y}{d x}=\frac{4 x^{3}}{\cos (y)}$ $\newline$ Choose $1$ answer: $\newline$ (A) $y=\arccos \left(4 x^{3}\right)+C$ $\newline$ (B) $y=\arccos \left(4 x^{3}+C\right)$ $\newline$ (C) $y=\arcsin \left(x^{4}+C\right)$ $\newline$ (D) $y=\arcsin \left(x^{4}\right)+C$

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Find derivatives of using multiple formulae

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Q. Solve the equation.

\newline

\frac{d y}{d x}=\frac{4 x^{3}}{\cos (y)}

\newline

Choose

1

answer:

\newline

(A)

y=\arccos \left(4 x^{3}\right)+C

\newline

(B)

y=\arccos \left(4 x^{3}+C\right)

\newline

(C)

y=\arcsin \left(x^{4}+C\right)

\newline

(D)

y=\arcsin \left(x^{4}\right)+C

Separate variables $x$ and $y$ : To solve the differential equation $\frac{dy}{dx}=\frac{4x^{3}}{\cos(y)}$ , we need to separate the variables $x$ and $y$ . This means we want to get all the $y$ terms on one side of the equation and all the $x$ terms on the other side.
Multiply by $\cos(y)$ : We multiply both sides by $\cos(y)$ to get $\cos(y) \, dy = 4x^3 \, dx$ .
Integrate both sides: Now we integrate both sides of the equation. The left side with respect to $y$ and the right side with respect to $x$ .
Apply inverse sine: The integral of $\cos(y)$ $dy$ is $\sin(y)$ , and the integral of $4x^3$ $dx$ is $x^4$ . So we have $\sin(y) = x^4 + C$ , where $C$ is the constant of integration.
Final solution: To solve for $y$ , we take the inverse sine (arcsin) of both sides. $y = \arcsin(x^4 + C)$
Final solution: To solve for $y$ , we take the inverse sine (arcsin) of both sides. $y = \arcsin(x^4 + C)$ Looking at the answer choices, we see that option (C) $y=\arcsin(x^{4}+C)$ matches our solution.