Differentiation practice I

Compute the derivative.

f[x_] = (x^15) + 4 (x^13) + 5 (x^7) + 3 x + 4; 
(∂_x) f[x]

Compute the derivative.

f[x_] = (3/((x^3) + 2 x + 5)); 
(∂_x) f[x]

Compute the derivative.

f[x_] = (((x^2) - 4)/((x^2) + 4)); 
(∂_x) f[x]
Together[%]

Compute the derivative.

f[x_] = (((x^2) + 3 x + 5)/((x^2) + 4));
\(Together[∂\_x f[x]]
\)

Simplify first,  then compute the derivative.

f[
          x_] = (((x^3) - (1/((x^2) + 1)))/((x^4) + (1/((x^2) + 1))));
g[x_]  :=  Simplify[f[x]]
g[x]

Together[(∂_x) g[x]]

Simplify first, then compute the derivative.

f[x_] = (1/(1 - ((2 x)/((x^2) + 1))));
g[x_]  :=  
        Simplify[f[x]];
g[
      x]
Together[(∂_x) g[
          x]]

Compute the derivative.

f[x_] := (x^(1/7)) + 3 (x^13) + (1/(x^(1/7))); 
(∂_x) f[x]

Compute the derivative.

f[x_]:=(((x^(1/7)) + 3 (x^13))/((x^(1/4)) + 2 (x^4)))
(∂_x) f[
        x]
Together[%]

Compute the derivative.

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

Compute the derivative.

f[x_] = (1/(Sqrt[(x^2) + 1])); 
(∂_x) f[x]

Compute the  derivative.

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

Compute the derivative

f[x_] = Sin[x] ((x^15) + 4 (x^13));
(∂_x) f[x]

Compute the derivative.

f[x_] = Sin[x]^2 ((x^15) + 4 (x^13)); 
(∂_x) f[
        x]

Compute the derivative.

f[x_] = Tan[x]/((x^3) + 2 x + 5);
\(∂\_x f[x]
\)

Compute the derivative.

f[x_] = Sin[x] Cos[x]; 
(∂_x) f[x]

Compute the derivative.

f[x_] := Sin[x] (E^x);
(∂_x) f[x]

Compute the derivative.

f[x_] = ((E^x)/Sin)[x];
(∂_x) f[x]
Simplify[(∂_x) f[
          x]]

Compute the derivative.

f[x_] = Sin[x]/((x^2) + 4); 
(∂_x) f[x]
Simplify[(∂_x) f[x]]

Compute the derivative.

f[x_] = (((x^2) + 3 x + 5)/Cos)[x]; 
\(∂\_x f[x]
\)

Compute the derivative.

f[x_] = ((((x^2) + 2) Sec[x])/((x^5) - (x^3) + 1)); 
(∂_x) f[x]
Simplify[%]

Compute the  derivative.

f[x_] = Tan[(1/(Sqrt[(x^2) + 1]))]; 
(∂_x) f[x]

Compute the derivative.

f[x_] = Log[Sin[x]^2 + 5]; 
(∂_x) f[x]

Compute the derivative.

f[x_]=(E^(Sin[x]^2 + 5));
(∂_x) f[
        x]

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

f[x_] = Log[10, x]; 
(∂_x) f[x]

Compute the derivative.

f[x_] = (10^((Sqrt[(x^2) + 1]))); 
(∂_x) f[x]

Compute the  derivative.

f[x_] = (Sqrt[(10^x) + 1]); 
(∂_x) f[x]

Compute the derivative.

f[x_] = ((((E^(-x)) + (E^x)))^5); 
(∂_x) f[x]

Compute the derivative.

f[x_] = (Sqrt[(Sqrt[Sin])[x] + 1]); 
(∂_x) f[x]

Compute the derivative.

f[x_] = (((x^2) + 3 x + 5)/Cos)[x]; 
(∂_x) f[x]

Compute the derivative.

f[x_] = ((((x + 1))^11)/(((x - 1))^11)); 
Simplify[Together[(∂_x) f[x]]]