Summary

Introduction to differentiation: Conclusion introduction to differentiation

Summary

In this chapter you have become acquainted with the notion of derivative of a function and you have learned what the derivatives of several standard functions are. This is summarized in the table below.

function	derivative
#f(x)=c# (a constant)	#f'(x)=0#
#f(x)=x^n#, where #n# is a natural number	#f'(x)=nx^{n-1}#
#f(x)=x^a#, where #a# is a real number, for #x\gt0#	#f'(x)=ax^{a-1}#
#f(x)=\exp(x)#	#f'(x)=\exp(x)#
#f(x)=a^x#, where #a\gt0#	# f'(x)=a^x\cdot\ln(a)#
#f(x)=\ln(x)#, for #x\gt0#	#f'(x)=\frac{1}{x}#
#f(x)= \log_a(x)#	#f'(x)=\frac{1}{x \cdot \ln(a)}#