Suppose that y = d(t) represents the distance that an object travels in time t. What does Ad represent?

Q: Calculate the derivative.

A: h(t)=t(t+1)(t2+1)

Q: The position of an object at time t is given by s(t) = -9 - 3t. Find the instantaneous velocity at t…

A: We can find the instantaneous velocity as below

Q: Find the derivative df/dk. " f (k) = ek + a*

A: Find the derivative of the given function.

Q: Find the given derivative. 1 D 2x 3 DX 2x 5

A:

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3 +2x2 y 5 =1

A: Product rule of differentiation:If f(x) is a function of u and v where both u and v are variables…

Q: Compute the derivative: d 4 dx x2 5 x=1 The derivative is:

A: The solution of the problem is given in the next step.

Q: Let y = x sin(2x). (a) How fast is y changing at x = t? (b) Find an equation of the tangent line to…

A: Given y=x sin(2x)

Q: Find dy/dx and d²y/dx². For which values of t is the curve concave upward?

A: x = t2 + 1 y = et - 1 dy/dx = dy/dt ÷ dx/dt

Q: 2 5. x=- 1+t2 2 y=, t(1+t?)

A: Given: x=21+t2, y=2t(1+t2).

Q: dy Solve the derivative dx for the function: x = e'sint ; y = etcost

A:

Q: Find the (a) derivative y'= dy dx y = (n² + 5 secx) ㅠ of following Question tog 3 x

A: Note: Due to guidelines i can solve only your first question. Solution: a) y=πe+5sec xlog3x…

Q: 1. Find for y defined implicitly by the equation dx

A:

Q: Find the derivative. y = In(t5t)

A: Consider the given equation y=lnt5t and simplify it. Use the logarithmic properties to simplify it.…

Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

A:

Q: Find the equation of the tangent line to y = e¯4t at t = 0.

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Q: dy of the following implicit functions. dx Find ху - Зу 10x 3.

A:

Q: Let y= 9 x5 – 1. Find A, B, and C so that dY = AxB + C. A В C = Then find the value of the…

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Q: Find dy/dx and dy/dx². x = e, y = tet For which values of t is the curve concave upward? (Enter your…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: sketch the shifted exponential curves y = 1 - ex and y = 1 - e-x

A: Given  The parent exponential function y=1-ex . To find the graph of the exponential function…

Q: What is the decreasing and what is the constant

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Q: Find the derivative. y = In /x+7 y' = D

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Q: Find dy/dx and d²y/dx². x = e', y = te"t dx dx2 For which values of t is the curve concave upward?…

A:

Q: Evaluate the function: dx ¤(1+x?)

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Q: Q3/ Find dy/dx at the given point for the following function

A: Introduction: In mathematics, differentiation is the process of determining the derivative, or rate…

Q: at e t

A:

Q: find dy/dx for the given value of x.

A: Finding dy/dx

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3 +2x2 y 5=1

A: Differentiate the given equation with respect to x.

Q: Find the equation of a curve having a slop by dy xy? у 3 ху? —, x > 0 dx and passing through the…

A:

Q: Find the derivatives of the functions s =√t/1 + √t

A: The function is s=t1+t.   Differentiate the function with respect to t.…

Q: dy Solve the derivative for the function x arcsin e', y = v1 – e2t. dx

A:

Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOLUTION): 2 X = 2…

A: First, evaluate the first derivative dydx (y'). To find y', determine the dxdt and dydt.…

Q: 19. e* +e = e**y

A: Solution ) ex + ey = ex + y  Differentiate with respect to x d/dx ( ex + ey )  = d/dx ( ex + y ) […

Q: Find dy/dx and d²y/dx². x = e', y = tet dy dx dy dx2 For which values of t is the curve concave…

A: Given a parametric equation,

Q: d -y(x) if e²-y = sin a d.x

A: We will solve the following

Q: Find the indicated derivative. dy if y %3D - 3х xp dy dx %3D

A: Recall: dα f(x)dx=α d[f(x)]dx; where, 'α' is any constant. dxndx=n.xn-1

Q: Find the derivative. y = In /x+5 y' =D

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Q: Find derivative of the 6tanx following function d d.x

A:

Q: Find dy/dx and d²y/dx². х %3еt, у3 te-t dy dx dzy dx2 For which values of t is the curve concave…

A: Given

Q: Assuming that y is defined implicitly by the equation a2 – y² = 61, the derivative dy at - dx (2,…

A:

Q: 5. x= y= t2-1

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Q: T* dx from a=-1 to b-1 is an even function.

A:

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. −4x2 −3x−1=y2 −y

A: The given function is,

Q: Find (a) the derivative , y = dy 4 -32x

A:

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3+2x2y5=1

A: The given equation is,

Q: • Find a formula for the nth derivative of y = 47ª, telling me how you decide what to do at each…

A:

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below y= 3 (Arccos…

A: Given function, y=3cos-1(2x)x(lnx)

Q: Find the equation of the tangent line.

A: We have to find the slope at (0,2)For that we need g'(0)

Q: Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

A: The given function is y=t+sin t    for  0≤t≤2π. Sketch the graph of the above function as shown…

Q: d (2a*e" + 4a*) dx Calculate the derivative:

A: