Question

differentiate the sinlog(x^3+1)

Answer 1

$Answer \: \: \\ \\ let \: \: \: \: y = \sin( log(x {}^{3} + 1) ) \\ \\ Differentiate \: \: Both \: sides \: \: with \: \\ respect \: \: to \: x \: we \: have \\ \\ \frac{dy}{dx} = \cos( log(x {}^{3} + 1) ) \times \frac{1}{(x {}^{3} + 1) } \times 3x {}^{2} \\ \\ \frac{dy}{dx} = \cos( log(x {}^{3} + 1 ) \times \frac{3x {}^{2} }{(x {}^{3} + 1)} \\ \\ Note \: \: \: \: \\ \\ \: if \: \: y = f(g(x)) \\ \\ then \: \: \: \: \frac{dy}{dx} = \frac{d(f(g(x))}{dx} \times \frac{d(g(x))}{dx} \\ by \: chain \: rule \: of \: Differentiation.$