a) A curve has equation y = x² cos x, x ER. Evaluate the gradient of the curve at x = π. Give the answer in terms of . dy dx ||

Q: Use implicit differentiation to determine Answer dx for the equation x + y² = 9. dy dx ||

A: Solution    Given that equation is

Q: Find the derivative of the function. 1 In(1 + 49x 14 y = x arctan 7x dy

A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

Q: Find the derivative. x10 12) y = cos /t dt

A: We differentiate both sides with respect to x

Q: Show that the slope dy/dx is defined at every point on the graph of 2y = x² + sin y.

A: Given- 2y=x2+sinx To prove- That the slope dydx is defined at every point on the graph of the above…

Q: Use a computer algebra system to plot y2 = x 3 - 4x for x and y between -4 and 4. Show that if dx /…

A: y2=x3-4x

Q: Calculate the derivative indicated. d²y dx2 where 1 y= 6- x=3 + 3x² x3 Answer: Submit answer Next…

A: Given:y=6x31​+3x2In the given, we are asked for dx2d2y​ which means we get the derivative two times,…

Q: Find the derivative d cos t dt dz

A: Given : ddx∫0xcostdt

Q: dy in each part. dr Find and simplify a) Use implicit differentiation 2x5 – y + 4ry³ = -8

A:

Q: Find the second derivative of y = 6xcosx.

A:

Q: dy given the equation 2² + y° = e". Use implicit differentiation to determine dr dy da ||

A: The equation is given by x2 + y5 = ey To evaluate : dydx

Q: Consider the function g(x): y = x² • V3- 2x. a) State the domain of the function. dy b) Determine dx…

A:

Q: Compute the derivatives. Use the fact that e2+x = e2 . ex to find d/dx (ex+2).

A: ddxex+2

Q: compute the derivative : y = cos(cos(cos(θ)))

A: the given function is: y=coscoscosθ we have to find the derivative of the given function.

Q: find dy/dx ,y= cosx

A:

Q: Use implicit differentiation to find and using the following equation. dx x² + 2y² = 9

A:

Q: (b) Find the derivative, d af sin dr sin (vt) dt.

A:

Q: Compute the derivative, and simplify your answer. You must show your work. t3/2 +t1/2 dt d dx

A: