Derivadas básicas

Si f(x)=k

• f'(x)=0

• f'(x)=x

• f'(x)=k

• f'(x)=1

• f'(x)=kx

Si f(x)=x

• f'(x)=x

• f'(x)=kx

• f'(x)=1

• f'(x)= $\frac{x^2}{2}$

• f'(x)=0

f(x)= 5x + x²

• f'(x)= 5 + x²

• f'(x)= 5 + x

• f'(x)= 5 + 2x

• f'(x)= 5 + 2x²

• f'(x)= 2x - 5

f(x) = x⁶

• f'(x)=x⁵

• f'(x)=x⁶

• f'(x)=6x⁵

• f'(x)=6x

f(x) = ln 3x

• $f'(x)=\frac{1}{x}$

• f'(x)= $\frac{1}{3x}$

• f'(x)=3x

• f'(x)=ln $\frac{1}{x}$

 $y\ =\log_a\ x$  

•  $\frac{1}{x\log_ax}$  

•  $\frac{1}{x\ln x}$  

•  $\frac{1}{x}$  

•  $\frac{1}{x\ln a}$  

f(x) = 3^x

• f'(x) = 3^x

• f'(x) = 3^x ln 3

• f'(x) = 3^x ln x

• f'(x) = $3^x$ $\log_3x$

f(x) = sen x y g(x) = cos x

• f'(x) = cos x y g'(x) = senx

• f'(x) = -cos x y g'(x) = senx

• f'(x) = cos x y g'(x) = -senx

• f'(x) = -cos x y g'(x) = -senx

f(x) = tg x

• f'(x) = $\frac{1}{\cos^2x}$

• f'(x) = $\frac{1}{sen^2x}$

• f'(x) = $\frac{1}{tg^2x}$

• f'(x) = $\frac{1}{sen^{ }x\ \cos\ x}$

f(x) = arc tg x

• f'(x)= $\frac{1}{x^2+a^2}$

• f'(x)= $\frac{1}{x^2-a^2}$

• f'(x)= $\frac{1}{x+a}$

• f'(x)= $\frac{1}{\sqrt{x^2+a^2}}$