Question

if y=sin^-1x,the value of dy/dx at y=pi/3 is​

Answer 1

Answer:

2

Step-by-step explanation:

y=sin^-1 x

x=siny

1=cosy dy/dx

dy/dx=1/cosy

dy/dx=1/(1/2)=2

Answer 2

Concept

Any equation with at least one derivative of an unknown function, whether it be a full or partial derivative, is referred to as a differential equation. If a function's rate of change with respect to x is, as we assume, inversely proportional to y, we can write it down as dy/dx = k/y.

Given

y = sin⁻¹x

Find

we need to solve the above expression by using the concept of differential equations get the value of dy/dx at y = π/3

Solution

we know that, y = sin⁻¹x

⇒ x = siny

differentiating on both sides

d/dx × x = d/dx × siny

1 = cosy dy/dx

dy/dx = 1/cosy

since dy/dx at  y = π/3

therefore dy/dx = 1/cos( π/3)

dy/dx =  2

hence we got the value of dy/dx at y =  π/3 as 2.

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