Question

12. Find the derivative of 2
${2}^{x} sinxlnx$​

Answer 1

Answer:

2^x( ln(2).ln(x)sinx + cosx.ln(x)+ (sinx/x))

Answer 2

Answer:

We know that,

When y=uvw, where u, v & w are functions

dy/dx=(vw)du/dx+(uw)dv/dx+(uv)dw/dx

Therefore,

$→y = {2}^{x} \sin(x)ln(x) \\ \frac{dy}{dx} = {2}^{x} ln(2) \sin(x) ln(x) + {2}^{x} \cos(x) ln(x) + \frac{ {2}^{x} \sin(x) }{x}\\ \boxed{\frac{dy}{dx} = {2}^{x} [ln(2) \sin(x) ln(x) + \cos(x) ln(x) + \frac{ \sin(x) }{x}]}✓$