Math 230/ W3dqs

Q1 . Writing the given enjoyments as composition of two functionsf (x (3x 2 )2 g (h (xwhere h (x 3x 2 and g (x x2Similarly , f (x 2x2 - 7 g (h (xWhere , h (x x2 - 7 /2 and g (x 2xOther examples of composite function arf (x 1 (1 x )2 g (h (xwhere h (x (1 x )2 and g (x 1 /xAlso , f (x 1 /Cosx g (h (xWhere h (x Cosx and g (x 1 /xQ (2 ) differential gear instrument of a elongated crew of two functions is the similar one-dimensional cabal of the first derivatives of the item-by-item(a) functionsExample 1Let us consider two functions g (x x2 and h (x 5x 2 at a time , permit us consider a function f (x ) which is a additive combination of g (x ) and h (xi .e .

f (x a g (x b h (x ax2 5bx 2b where , `a and `b ar constants Thus it can be seen that the derivative of a linear combination of two functions is the alike linear combination of the derivatives of the various(prenominal) functions instantly let us take another exampleExample 2Let us consider two functions g (x Sinx and h (x Cosx at once , let us consider a function f (x ) which is a linear combination of g (x ) and h (xi .e . f (x a g (x b h (x aSinx bCox where , `a and `b atomic number 18 constants Thus it can be seen that the derivative of a linear combination of two functions is the same linear combination of the derivatives of the individual functionsQ3 . Applying quotient rule for determining the derivative of the proportion of two functions Now quotient rule says if a function f (x ) can be represented a ratio of two functions g (x ) and h (x ) such that f (x g (x /h (x then its derivative is given as...If you want to charter a full essay, put it on our website: Ordercustompaper.com

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