Suppose u and v are functions of x that are differentiable at x=0 and that u(0)= 7,u'(0)=-5,v(0)= -1, v'(0)= -4. Find the values of the following derivatives at x=0.

This question is incomplete, the complete question is;

Suppose u and v are functions of x that are differentiable at x=0

and that { u(0) = 7, u'(0) = -5 }  { v(0)= -1, v'(0) = -4 }

Find the values of the following derivatives at x = 0.

a) ( uv )

b)  ( )

c)  ( )

a) ( uv ) = -23  

b) ( )  = 33

c) ( ) = -32/49 or - 0.6531

Step-by-step explanation:

Given that;

{ u(0) = 7, u'(0) = -5 }  { v(0)= -1, v'(0) = -4 }

a)

( uv )

we differentiate

( uv )  = uv' + vu'

at x = (0), we substitute our values

( uv ) = ( 7 × -4 ) + ( -1 × -5)

( uv )  = -28 + 5

( uv ) = -23  

b)

( )

we differentiate

( ) = ( vu' - uv' ) / v²

at x=0, we substitute our values

( ) = ( (-1 × -5) - (7 × -4 ) ) / (-1)²

( ) = (( 5 - ( -28 )) / 1

( )  = 33 / 1

( )  = 33

c) ( )

we differentiate

( )  = ( uv' - vu' ) / u²

at x=0, we substitute our values

( )  = ( (7 × -4) - (-1 × -4) ) / (7)²

( ) = ( -28 - ( 4 ) ) / 49

( )  = ( -28 - 4 ) /49

( )  = -32 / 49

( ) = -32/49 or - 0.6531

hard

step-by-step explanation:

ask the math teacher she or he would know lol.

step-by-step explanation: