Question

d/dx(sinx) find differntional

Answer 1

Here we have to find the differential of d/dx (sinx) 
d/dx(sinx) = cosx
Proof:
Let f(x) = sin x
So, f(x+h) = sin (x+h) where "h" is a very small quantity.
Since, we know that,
d/dx f(x) = limit (h→0) [ {f(x+h) - f(x)} / h ]
d/dx (sinx) = limit (h→0) [ { sin (x+h) - sinx } / h ]
d/dx (sinx) = limit (h→0) [ ( sinxcosh + cosxsinh - sinx ) / h ]
d/dx (sinx) = limit (h→0) [ sinx (cosh - 1) + cosxsinh ] / h
d/dx (sinx) = limit (h→0) [ sinx (cosh - 1) / h ] + limit (h→0) [ cosxsinh / h ]
d/dx (sinx) = 0 + cos x . limit (h→0) sinh / h
d/dx (sinx) = cos x (1)   [ ∵ limit (h→0) sinh / h = 1 ]
d/dx (sinx) = cos x 
Hence proved.