Question

find d/dx(sin^-1(3cosx+4sinx/5)

Answer 1

Answer:

dy/dx = (3sinx + 4cosx)/5 siny

y = cos⁻¹ (3cos x- 4sinx)/5

cos y = (3cos x- 4sinx)/5

5 cos y = 3cosx - 4sinx

now, apply differentiation

5(-sin y) (dy/dx) = 3(-sinx) - 4(cosx)

-5 sin y (dy/dx) = -3sinx -4cosx

now simplify equation, we get

dy/dx = (3sinx + 4cosx)/5 siny

Answer 2

$( - 3 \sin(x) + \frac{4 \cos(x) }{5} ) \\ \frac{1}{ \sqrt{1 - (3 \cos(x) + \frac{4 \sin(x) }{5} } ) {}^{2} }$