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Find (dy)/(dx) for the functions: y=x^3e...

Find `(dy)/(dx)` for the functions: `y=x^3e^xsinx`

Text Solution

Verified by Experts

The correct Answer is:
`x^(2)e^(x)(3 sin x + x sin x + x cos x )`
`y=x^(3)e^(x) sin x`
`therefore" " (dy)/(dx)=(d)/(dx)(x^(3)e^(x)sin x)`
`={(d)/(dx)(x^(3))}e^(x) sin x +x^(3){(d)/(dx)(e^(x))}sin +x^(3)e^(x){(d)/(dx)(sin x)}`
`=3x^(2)e^(x) sin x +x^(3)e^(x) sin x +x^(3) e^(x) cos x`
`=x^(2)e^(x)(3 sin x + x sin x + x cos x)`
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