Question

y = log (x4 sin2x) find dy/dx​

Answer 1

Answer:

y = log (x4 sin2x)

Step-by-step explanation:

$\frac{d}{dx} (y) =\frac{d}{dx} (log (x4 sin2x))\\= \frac{1}{x^{4}sin2x } *\frac{d}{dx} (x^{4}sin2x )\\=\frac{1}{x^{4}sin2x} (x^{4} \frac{d}{dx}(sin2x) +sin2x\frac{d}{dx}(x^{4} ) )\\=\frac{1}{x^{4}sin2x} (x^{4}cos2x \frac{d}{dx}(2x) + sin2x(4x^{3}) )\\\\=\frac{2x^{4}cos2x + 4x^{3}sin2x }{x^{4}sin2x }$

used formulas

d/dx(sinx)=cosx

d/dx(x^n)=nx^(n-1)

d/dx(logx)=1/x