If$f ( x ) = e ^ { x } g ( x ) \text {, and if } g ( 0 ) = 3 \text { and } g ^ { \prime } ( 0 ) = - 2 \text {, find } f ^ { \prime } ( 0 ) \text {. }$

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The Answer of If$f ( x ) = e ^ { x } g ( x ) \text {, and if } g ( 0 ) = 3 \text { and } g ^ { \prime } ( 0 ) = - 2 \text {, find } f ^ { \prime } ( 0 ) \text {. }$

If $f ( x ) = e ^ { x } g ( x ) \text {, and if } g ( 0 ) = 3 \text { and } g ^ { \prime } ( 0 ) = - 2 \text {, find } f ^ { \prime } ( 0 ) \text {. }$

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If f(x)=exg(x), and if g(0)=3 and g′(0)=−2, find f′(0). f ( x ) = e ^ { x } g ( x ) \text {, and if } g ( 0 ) = 3 \text { and } g ^ { \prime } ( 0 ) = - 2 \text {, find } f ^ { \prime } ( 0 ) \text {. }f(x)=exg(x), and if g(0)=3 and g′(0)=−2, find f′(0).

Definitions:

If $f ( x ) = e ^ { x } g ( x ) \text {, and if } g ( 0 ) = 3 \text { and } g ^ { \prime } ( 0 ) = - 2 \text {, find } f ^ { \prime } ( 0 ) \text {. }$