Differentiate the following w.r.t.x.
a. `9`
b. `pi^4`
c. `2e^3` d. `x^2+5`
e. `(x+5)^(-1//2)` f. `5x^(3//2)`
g. `sqrt(x+3)`
h. `(2x^2+9)^3`

Explanation

a. `(d)/(dx)(9)=0`, since the differentiation of constant is zero.
b. `(d)/(dx)(pi^4)=0`, since the differentiation of constant is zero.
c. `(d)/(dx)(2e^3)=0`, since the differentiation of constant is zero.
d. `(d)/(dx)(x^2+5)=2x+0=2x`
e. `(d)/(dx)[(x+5)^(-1//2)]=-1/2(x+5)^(-3//2)`
f. `(d)/(dx)(5x^(3//2))=5(d)/(dx)(x^(3//2))=5xx3/2x^(1//2)=15/2x^(1//2)`
g. `(d)/(dx)(sqrt(x+3))=(d)/(dx)[(x+3)^(1//2)]=1/2(x+3)^(-1//2)`
h. (d)/(dx)[(2x^2+9)^3]=3(2x^2+9)^2(4x)=12(2x^2+9)^2x`