How do you differentiate #e^(-10x)#?

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Answer 1 · 2018-06-11T00:24:59

#-10e^(-10x)#

Given: #e^(-10x)#.

Use the chain rule, which states that,

#dy/dx=dy/(du)*(du)/dx#

Let #u=-10x,:.(du)/dx=-10#.

Then, #y=e^u,:.dy/(du)=e^u#.

Combining, we get:

#dy/dx=e^u*-10#

#=-10e^u#

Substitute back #u=-10x# to get the final answer:

#=-10e^(-10x)#

Note:

A common fact in derivatives is that #d/dx(e^(f(x)))=f'(x)e^(f(x))#.

Answer 2 · 2018-06-11T00:26:31

#d/dx(e^(-10x))=-10*e^(-10x)#

By the formula #(d(e^u))/dx=e^u*(du)/dx#

#d/dx(e^(-10x))=e^(-10x)*(d(-10x))/dx#

#d/dx(e^(-10x))=e^(-10x)*(-10)#

#d/dx(e^(-10x))=-10*e^(-10x)#

I hope the explanation is useful....God bless...