Find dz/dt. In(t) + In(z6) = 15 dz/dt = Find dy/dx: sin(xy) = 6x + 5 dy/dx = Fin

Question

Find dz/dt. In(t) + In(z6) = 15 dz/dt = Find dy/dx: sin(xy) = 6x + 5 dy/dx = Find the slope of tangent line to the curve at the point (1,2). x3 + 5x2y + 2y2 = 4y+ 11 Find the equation of the tangent line to the curve y = / y + b at the point(0,0). Your answer will have b in y(x) = Consider the curve defined by x2 + y2 - 5x + 13/ = 19. Find dy/dx. dy/dx = Under what condition on x is the tangent line to the curve horizontal? Give an exact answer. x = Under what condition on y is the tangent line to the curve vertical? Give an exact answer. y =

Explanation / Answer

1)

1/t +(1/z^6)6z^5 dz/dt=0

dz/dt=-z/6t

5)

sinxy=6x+5

cosxy (xdy/dx+y)=6

dy/dx=([6/cosxy]-y)/x

6)

3x^2 + 5x^2y'+10yx+4yy'=4y'

at (1,2)

3+5y'+20+8y'=4y'

y'=-23

7)y=x/(y+b)

y^2+yb=x

2yy'+by'=1

at(0,0)

y'=1/b

tangent is

y-0=1/b(x-0)

8)2x+2yy'-5+13y'=0

y'=(5-2x)/(2y+13)

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