5ex+2?

d/dx(u+v)=du/dx+dv/dx

d/dx(5ex+2)=d/dx(5ex)+d/dx(2)

-The derivative of 5ex is:

d/dx(cu)=c*du/dx where c is a constant.

d/dx(5ex)=5*d/dx(ex)

-The derivative of 2 is 0 because it is a constant.

d/dx(5ex+2)=(5*d/dx(ex))+(0)

d/dx(5ex+2)=5*d/dx(ex)

-The derivative of ex is:

d/dx(eu)=eu*d/dx(u)

d/dx(ex)=ex*d/dx(x)

d/dx(5ex+2)=5*(ex*d/dx(x))

-The derivative of x is:

d/dx(xn)=nxn-1

d/dx(x)=1*x1-1

d/dx(x)=1*x0

d/dx(x)=1*(1)

d/dx(x)=1

d/dx(5ex+2)=5*(ex*1)

d/dx(5ex+2)=5*(ex)

d/dx(5ex+2)=5ex

5ex+2?

d/dx(cu)=c*du/dx where c is a constant.

d/dx(5ex+2)=5*d/dx(ex+2)

-The derivative of ex+2 is:

d/dx(eu)=eu*d/dx(u)

d/dx(ex+2)=ex+2*d/dx(x+2)

d/dx(5ex+2)=5*(ex+2*d/dx(x+2))

-The derivative of x+2 is:

d/dx(u+v)=du/dx+dv/dx

d/dx(x+2)=d/dx(x)+d/dx(2)

d/dx(5ex+2)=5*[ex+2*(d/dx(x)+d/dx(2))]

-The derivative of x is:

d/dx(xn)=nxn-1

d/dx(x)=1*x1-1

d/dx(x)=1*x0

d/dx(x)=1*(1)

d/dx(x)=1

-The derivative of 2 is 0 because it is a constant.

d/dx(5ex+2)=5*[ex+2*(1+0)]

d/dx(5ex+2)=5*[ex+2*(1)]

d/dx(5ex+2)=5*[ex+2]

d/dx(5ex+2)=5ex+2

x5lnx?

d/dx (uv)=u*dv/dx+v*du/dx

d/dx (x5lnx)=x5*[d/dx(lnx)]+lnx*[d/dx(x5)]

-The derivative of lnx is:

d/dx(lnu)=(1/u)*[d/dx(u)]

d/dx(lnx)=(1/x)*[d/dx(x)]

d/dx(lnx)=(1/x)*[1]

d/dx(lnx)=(1/x)

-The derivative of x5 is:

d/dx (xn)=nxn-1

d/dx (x5)=5x5-1

d/dx (x5)=5x4

d/dx (x5lnx)=x5*[1/x]+lnx*[5x4]

d/dx (x5lnx)=[x5/x]+5x4lnx

d/dx (x5lnx)=x4+5x4lnx