Question

calculate the value dy/dx in the point x=90 when y=x^sinx +(x)^1/2​

Answer 1

Now use log

log y= log x^sinx+log x^1/2

log y= sinx log x + 1/2 log x

Now differentiate

d(logy)/dx= d(sinx logx)/dx + 1/2d(logx)/dx

1/y dy/dx = sinx d(logx)/dx+logx d(sinx)/dx+1/2x

1/y dy/dx = sinx/x + cosx logx + 1/2x

dy/dx= y[sinx/x + cosx logx + 1/2x]