Derivative Rules 1

The derivative of a constant function, f(x) = c is

• 0

• 1

• -1

• DNE

The derivative of the function, f(x) = x is

• 0

• 1

• -1

• DNE

The derivative of the function, f(x) = e^x

• e^x

• -e^x

• -e^-x

• e^-x

The derivative of the function, f(x) = sin(x)

• cos(x)

• -sin(x)

• tan(x)

• sec²(x)

The derivative of the function, f(x) = cos(x)

• cos(x)

• -sin(x)

• tan(x)

• sec²(x)

The derivative of the function, f(x) = xⁿ

• f ' (x) = nxⁿ

• f ' (x) = nx^n-1

• f ' (x) = x^n-1

• f ' (x) = n-1xⁿ

The derivative of the function, f(x) = axⁿ

• f ' (x) = anxⁿ

• f ' (x) = ax^n-1

• f ' (x) = anx^n-1

• f ' (x) = a-1x^a

The derivative of the function, f(x) = ln(x)

• $f'\left(x\right)\ =\ \ln\left(x\right)$
  

• $f'\left(x\right)=e^x$

• 
  

  $f'\left(x\right)=\frac{1}{x}$

The derivative of the function, f(x) = aln(x)

•  $f'\left(x\right)=a\ln\left(x\right)$  
  

•  $f'\left(x\right)\ =ae^x$  
  

•  $f'\left(x\right)=\frac{a}{x}$  

The derivative of the function, f(x) = ae^x

• ae^x

• -ae^x

• -ae^-x

• ae^-x