Find the derivatives of the function w.r.t X 

Y = 5^logsinx +(Sinx)^x

Asked by evanbose3 | 5th Jul, 2019, 10:28: PM

Expert Answer:

y = 5logsinx +(Sinx)x
Let u = 5log sinx and v = (sin x)x
u = 5log sinx
du/dx = 5log sinx log 5 × (1/sinx) × cosx
du/dx = 5log sinx log 5 ×cotx ...(i)
v = (Sinx)x
log v = xlog sinx
1/v dv/dx = x (1/sinx) cosx + log sinx
dv/dx = (Sinx)x (xcotx + log sinx)
To get dy/dx add (i) and (ii)
dy/dx = 5log sinx log 5 ×cotx + (Sinx)x (xcotx + log sinx)

Answered by Sneha shidid | 6th Jul, 2019, 09:22: PM