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How do you find the derivative of #f(z)=e^z(cosz)#?

Answer 1

Emilia Aguilar

#f'(z)=e^z(cosz-sinz)#

apply the product rule

#f'(z)=d/dz(e^z)*cosz+d/dz(cosz)*e^z#

#f'(z)=e^z*cosz-sinz*e^z#

#f'(z)=e^z(cosz-sinz)#

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Answer 2

Charles Arocha

To find the derivative of ( f(z) = e^z \cos(z) ), you can use the product rule, which states that if ( u ) and ( v ) are functions of ( z ), then the derivative of ( u(z) \cdot v(z) ) with respect to ( z ) is ( u'(z) \cdot v(z) + u(z) \cdot v'(z) ). Applying this rule, the derivative of ( f(z) ) is ( e^z \cdot \cos(z) - e^z \cdot \sin(z) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.