How do you differentiate #(sqrt x)(x^2+3sinx)#?
Using differentiate product rule
See explanation below
We know that in functions product, de derivative is (derivative of a product)
Thus we have (if
If we apply prior formula we have
Product rule is
Obviously we already have f(x) and g(x) so we just need to find the derivatives of both
To derive the 3sin(x) you would have to use product rule again where f(x)=3 and g(x)=sin(x), but remember the derivative of a plain number is zero, so all that's left of product rule is #f(x)*g'(x), which is just 3cos(x),remember the derivative of sin is cos.
Now just plug all the parts yo have into product rule to get: