Question

Differentiate the following with respect to `x :` (i) `x^3e^xsinx` (ii) `xsinxlogx` (iii) `x^n(log)_a xe^x`

Answer 1

1)`x^3e^xsinx`
`d/dx(x^3e^xsinx)`
`e^xsinxd/dx(x^3)+x^3sinxd/dx(e^x)+x^3e^xd/dx(sinx)`
`3x^2e^xsinx+x^3e^xsinx+x^3e^xcosx`
2)`xlogxsinx`
diff with respect to x
`sinxlogx+xcosxlogx+xsinx*1/x`
`sinx-sinxxlogx+xcosxlogx`.