Differentiation practice II

Compute the derivative.

f[x_] = (x^5) + π (x^(1/7))
(∂_x) f[x]

Compute the derivative.

f[x_] =  x^3  +  3 (x^2  +  π^2)
(∂_x) f[x]

Compute the derivative.

f[x_] = (((x + 1))^2) ((x^3) - 5)
(∂_x) f[x]
Expand[%]

Compute the derivative.

f[θ_] = ((((θ^2) + Sec[θ] + 1))^3)
(∂_θ) f[θ]

Compute the derivative.

f[t_] = ((Sqrt[t])/(1  + (Sqrt[t])))
(∂_t) f[t]
Together[%]

Compute the derivative.  Remark: the traditional way of writing this function would be 
 \(TraditionalForm\`\(\(
\)\(f(x) = 
        2\ \(\(tan\^2\)(x)\) - 2\ \(\(sec\^2\)(x)\)\)\)\)

f[x_] = 2 Tan[x]^2 - 2 Sec[x]^2
(∂_x) f[x]

Compute the derivative.  The traditional way of writing this function would be  
(1/((sin^2)(x))) - (π/(sin(2 π x)))

f[x_] := (1/Sin)[x]^2 - (π/Sin)[2 π x]
(∂_x) f[x]

Compute the derivative.   The traditional way of writing this function would be

(cot^3)((2/(t^2)))

f[x_] := Cot[(2/(t^2))]^3
(∂_t) f[t]

Compute the derivative.

f[θ_] =  Sin[(Sqrt[2  θ])]
(∂_θ) f[θ]

Compute the derivative.

f[x_] = (1/2) (x^2) Cot[x]^2
(∂_x) f[x]

Compute the  derivative.  The traditional form of the function would be
(Sqrt[x]) 2 csc((((x + 1))^3))

f[x_] := (Sqrt[x]) 2 Csc[(((x + 1))^3)]
(∂_x) f[x]

Compute the derivative.  The traditional form of the function would be
(Sqrt[x]) 2 (csc^3)(x + 1)

f[x_] = (Sqrt[x]) 2 Csc[x + 1]^3
(∂_x) f[x]

Compute the derivative.  The tradtional form of the function woud be

(((sin^2)((x^3)))/(x^2))

\(f[x_] = Sin[x\^3]\^2\/x\^2\)
(∂_x) f[x]

Compute the derivative.

f[θ_] =  Sin[θ]/(Cos[θ]  + 1)
(∂_θ) f[θ]
\(Together[%]
\)

Compute the derivative.

f[θ_] =  ((Sin[π/2] Sin[θ])/(Cos[θ]  + 1))
\(∂\_θ 
        f[θ]

\)

Compute the derivative.

f[x_] := Sin[x] (Sqrt[(x^2) + 1]) (E^x)
(∂_x) f[x]

Compute the derivative.

f[x_] = Cos[(E^((x^2)))]
(∂_x) f[x]

Compute the derivative.

f[x_] = Sin[E x]/(x^2)
(∂_x) f[x]
Together[(∂_x) f[x]]

Compute the derivative.  The traditional form would be

(((sin^2)(e x))/(x^2))

\(f[x_] = Sin[E\ x]\^2\/x\^2\)
(∂_x) f[x]

Compute the derivative.

f[x_] = Log[(E^x)]; 
(∂_x) f[x]

Compute the  derivative.

f[x_] = Tan[ Log[x]];
(∂_x) f[x]

Compute the derivative.

f[x_] =  Cos[x]/x   +  (x/Cos)[x]
(∂_x) f[x]
Together[%]

Compute the derivative.

f[x_] =  ((1  +  Csc[x])/(1  -  Csc[x]))
(∂_x) f[x]
Together[%]

Compute the derivative.  Log[10,x] means log base 10 of x.

f[x_] = Log[10, (x^3)]; 
(∂_x) f[x]

Compute the derivative.

f[x_] = 
      A (E^(-α x)) + 
        A (E^(β x))
(∂_x) f[x]