Question

The derivative of f(sinx) w.r.t.x, when f(x)=logx is

Answer 1

• Given :

f(sinx) w.r.t.x,

• when f(x)=logx

Here

• f(sinx)

f(x) = logx

f(sinx) = log(sinx)

Or

y = log(sinx)

• Let's differentiate w. r. t. x
• Apply chain rule

dy/dx = d{log(sinx)}/d(sinx) . d(sinx)/dx

• Differentiation of logx = 1/x
• sinx = cosx

dy/dx = 1/sinx . cosx

dy/dx = cosx/sinx

• cosx/sinx = cotx

dy/dx = cotx

Answer 2

Answer:

⏩REQUIRED ANSWER:

f(sinx)

f(x) = logx

f(sinx) = log(sinx)

• y = log(sinx)

♂️Now, Apply chain rule--

• dy/dx = d{log(sinx)}/d(sinx)/dx

➡️dy/dx = 1/sinx ; cosx

➡️dy/dx = cosx/sinx

➡️cosx/sinx = cotx

➡️dy/dx = cotx