Question

If y is differentiable function of x, then find derivative of sin y w. r. t. x.​

Answer 1

Answer:

Step-by-step explanation:

d(siny)/dx =  (cosydy)/dx

Answer 2

If $y$ is differentiable function of $x$ ,$\frac{dy}{dx} x=siny$ is   $\frac{dy}{dx} =sec(y)$.

Step by step explanation:

$x=sin y$

differentiate  both side of the equation,

$\frac{d}{dx} ( x) =\frac{d}{dx} sin(y)$

Use the power rule to distinguish yourself, which states that

$\frac d{dx}(x^n)\;$ is $nx^{n-1}$ where $n=1$

the right side of the equation should be differentiated

$\cos\;(y)\frac d{dx}(y)$

Set the left side equal to the right side to reform the equation.

$1=\cos(y)y^'$

solve for $y^'$

$y^' =sec(y)$

replace $y^'$ with$\frac{dy}{dx}$

$\frac{dy}{dx} =sec(y)$