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Find the derivastive of the following functions with respect to x. a. `y=x^2 sinx, b. `y= (sin x)/x and c. y=sin (x^2)` |
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Answer» `y=x^2 sin x` `dy/dx= x^2 d/dx(sinx)+(sinx) d/dx (x^2)` `=x^2cosx+(sinx)(2x)` `=x(2sinx+x cosx)` b. `y=(sinx)/2` dy/dx= (x d/dx(sinx) - sin x(dx/dy))/x^2` `=(x cosx-sinx)/x^2` `dy/dx=d/dx^2(sinx^2).(d(x^2))/dx` `=2x cos x^2`. |
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