-Use implicit differentiation to find dy/dx where x2y2 + x cos(y) = 6 -Use logarithmic differentiation...

-Use implicit differentiation to find dy/dx where x²y² + x cos(y) = 6

-Use logarithmic differentiation to find the derivative of o(x) = (cos(x))^ln(x)

-Find the first and second derivatives of p(x) = 6 ln(x²+3x)

-A balloon is rising vertically at a constant speed of 5 ft/sec. A boy is

cycling along a straight road at a speed of 15 ft/sec. When he passes

under the balloon, it is 45 ft above him.How fast is the distance between

the boy and the balloon increasing 3 seconds later?

Expert Solution

milcah answered 2 years ago

Find dy/dx by implicit differentiation: cos(x+y)=y^3 sin x

Find dy/dx by implicit differentiation. 3x^6+x^5y−2xy^6=8

part 1) Find dy/dx by implicit differentiation. 3x^6+x^5y−2xy^6=8 dy/dx= part 4) A campground owner has 2000 meters of fencing. She wants to enclose a rectangular field bordering a lake, with no fencing needed along the lake: see the sketch. a) Write an expression for the length of the field: 2000-x (this is correct) b) Find the area of the field (length times width): -x^2+2000x (this is correct) c) Find the value of x leading to the maximum area: d)...

Use implicit differentiation to find ∂z/∂x and ∂z/∂y if xz = cos (y + z).

Use implicit differentiation in each of the following problems to find dy/dx. Then determine the equation...

Use implicit differentiation in each of the following problems to find dy/dx. Then determine the equation of a tangent line at the given point. (a) y = xe^y , at (1/e, 1) (b) sin x cos y = sin x + cos y, at (0, π/2). Hint: One of the lines is vertical, so its derivative is undefined at the given point. Recall that the equation of a vertical line has the form x = a.

Find dy/dx for a & b a) sin x+cos y=1 b) cos x^2 = xe^y c)Let...

Find dy/dx for a & b a) sin x+cos y=1 b) cos x^2 = xe^y c)Let f(x) = 5 /2 x^2 − e^x . Find the value of x for which the second derivative f'' (x) equals zero. d) For what value of the constant c is the function f continuous on (−∞,∞)? f(x) = {cx^2 + 2x, x < 2 , 2x + 4, x ≥ 2}

√xy+2x=√y . Use implicit differentiation to find y’.

Use implicit differentiation to find ∂z/∂x and ∂z/∂y. e4z = xyz

evaluate C (y + 4 sin x) dx + (z2 + 8 cos y) dy +...

evaluate C (y + 4 sin x) dx + (z2 + 8 cos y) dy + x3dz where C is the curve r(t) = sin t, cos t, sin 2t , 0 ≤ t ≤ 2π. (Hint: Observe that C lies on the surface z = 2xy.)

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln...

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln x +y/x)dx = (1-lnx)dy Solve (y^2+yx)dx - x^2dy =0 Solve (x^2+2y^2)dx = xydy Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2) Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2) Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2 Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0 Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1 6. Mixture Problem Initially 40 lb of salt is dissolved in a large...

Find dy/dx by implicit differentiation. 11. ycosx=x^2+y^2 13. sqrt(x+y)=x^4+y^4 15. tan(x/y)=x+y 17. sqrt(xy)=1+(x^2)*(y) 19. sin(xy) =...

Find dy/dx by implicit differentiation. 11. ycosx=x^2+y^2 13. sqrt(x+y)=x^4+y^4 15. tan(x/y)=x+y 17. sqrt(xy)=1+(x^2)*(y) 19. sin(xy) = cos(x+y)

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