1 of 1 Due: November 13, 2017 Make sure you show all work. No credit will be giv

Question

1 of 1 Due: November 13, 2017 Make sure you show all work. No credit will be given for answers no justification. Don't leave anything blank because partial credit c awarded. Work Alone! Please circle/box final answers and label pro clearly. Good luck! ) 1. Find the derivative of the following using the chain rule (a) (10 points) (22 3)7 (b) (10 points) rr2 - 4x)5 2. (15 points) Find the slope of the tangent line for the function y = (42.3-7p" + 2x2-4x at the point (0,0) 3. (10 points) For the function y 5x3-r4 (21+3)4, find 4. (15 points) Find y"(2) for y = 3x2-5x +x6. 5. Find dr implicitly for the following functions (a) (10 points) y2-ry +13-4x = 7 (b) ( 15 points) 2:2y + xy + 3x-4y2 =-1+ y 6. (15 points) Find the equation of the tangent line to ry +3y3-2t=_3 at (21)

Explanation / Answer

multiple questions posted.please post each question seperately

1)

formula:d/dx(f(x))n=n(f(x))n-1(f '(x)), profuct rule:(uv)'=u'v +uv'

a)

d/dx((2x2+x3)7)= (7(2x2+x3)7-1)(2*2x2-1 +3x3-1)

d/dx((2x2+x3)7)= (7(2x2+x3)6)(4x +3x2)

d/dx((2x2+x3)7)= 7x13(4 +3x)(2+x)6

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b)

d/dx(x2(x2-4x)5)= [2x2-1(x2-4x)5]+[x25(x2-4x)5-1(2x2-1-4*1)]

d/dx(x2(x2-4x)5)= [2x(x2-4x)5]+[5x2(x2-4x)4(2x-4)]

d/dx(x2(x2-4x)5)= [[2x(x2-4x)]+[5x2(2x-4)]](x2-4x)4

d/dx(x2(x2-4x)5)= [2x3-8x2+10x3-20x2](x2-4x)4

d/dx(x2(x2-4x)5)= [12x3-28x2](x2-4x)4

d/dx(x2(x2-4x)5)= 4x6(3x-7)(x-4)4

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2)

given y =(4x3-7x)3+2x2-4x

differentiate with respect to x

dy/dx= (3(4x3-7x)3-1(4*3x3-1 -7*1))+2*2x2-1-4*1

dy/dx= (3(4x3-7x)2(12x2 -7))+4x-4

at point (x,y) =(0,0)

dy/dx= (3(4*03-7*0)2(12*02 -7))+4*0-4

dy/dx= 0+0-4

dy/dx= -4

so the slope of tangent line is -4

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