2. Assume the length L (in centimeters) of a particular species of fish after t years is modeled by the following graph. LA dL represent and what happens to this derivative as t increases? dt a) What does b) What does the derivative tell you about how this species of fish grows? c) Sketch the graph of L' and L".

Q: Determine the equation of the curve whose tangent line at any point (x,y) is e- sin x and passes…

A:

Q: 16. Find the equation of the tangent line to the curve y = e* at the point (a, f(a)) when a = In 3.

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Find the derivative dydx of the logarithmic spiral defined by the equationr=f(θ)=aebθ,where a, b are…

A:

Q: What is the derivative of =pt? y=e eki?

A:

Q: Find the derivative with respect to 0: y = In(sec 0 + tan 0)

A: Here we have to find the derivative of             y=ln(secθ+tanθ) To find the derivative here we…

Q: 60. Find an equation of the tangent line to the graph of f(x) a) at (1, 1); b) at (3, 5); c) at…

A:

Q: The function f(r) = tanh(r) is one-to-one and so is invertible. Using our rule/ formula for relating…

A: Given that

Q: What is the equation of the line tangent to the curve e'+cos(x) = 1 at the point .0?

A:

Q: #36 Find the equation of the tangent line to the graph of X²(x²+y²) = y? at

A:

Q: Evaluate the derivative of the function. y= sec "(2 In 8x) dx

A:

Q: 4 1日4)+e dy=

A:

Q: 1 Find an equation of the tangent line to the graph of f(x) = c) at a) at (1,1); b) at 3, '27

A: Given - A Function To find - Its tangents at given points

Q: Find an equation of the line tangent to f(x) at the point |3D 1+e

A: Find slope at given point and then use formula  to find tangent line

Q: Find an equation of the tangent line to the graph of y = In(x2) at the point (3, In(9)). %3D *+2 ln…

A: y-y1=dydxx-x1

Q: Find an equation of the tangent line to the curve at the point (1, 1). y=ln(xe^x^9)  (e is raised…

A:

Q: The slope of the tangent line to the graph of x2 – y? = ln(xy) at the point (1, 1) is

A:

Q: Find the exact equation (without decimal approximations) of the tangent line in the form y = mx + b…

A:

Q: what is the derivative of arctan(u/1+4u)

A: To determine the first order derivative of the provided function.

Q: Consider the graph of y =JX) shown below in blue. Submit your answer to this question by completing…

A: To approximate the tangent line to the function.

Q: (플아 What is the equation of the line tangent to the curve e + cos(x) = 1 at the point ,0?

A:

Q: 8. Find the equation of the tangent line to the curve y = e* at the point (a, f (a)) when a = In 3.

A:

Q: Find an equation of the tangent line to the curve at the given point. y = 3ex cos x, (0, 3)

A: To find: The equation of the tangent line to the curve  at the given point0,3 Given information: The…

Q: 1. (a) Use implicit differentiation to find the slope of the tangent to the curve y? – xy +y + 2 = 0…

A: Given: The equation of the curve y2-xy+y+2=0

Q: What is the equation of the line tangent to the curve e' + cos(x) = 1 at the point (,0

A:

Q: When a question asks to compute dy/dx using the definition of the derivative, how do I approach it?

A:

Q: Find the derivative dydx of the logarithmic spiral defined by the equation r=f(θ)=aebθ, where a, b…

A:

Q: 7. Apply the appropriate rule to determine the slope of the tangent line to the curve graph given by…

A:

Q: Determine the equation of the curve whose tangent line at any point (x,y) is e* – sin x and passes…

A:

Q: Find the derivative of the given function. t q= tan Vi+2 dq dt

A: The following formulas of differentiation can be used to solve the given derivative. i d dttan…

Q: Give the equation of the tangent line to the graph of 3sin y − ln(e sech x) = tan−1(x2y) + x/3 at…

A:

Q: Find the slope of the tangent line to the function f(x) = tan(cos(ax)) at x =π/2a. Leave your answer…

A: According to chain rule of differentiation ddxfgx=f'gx·g'(x) . Now using this rule differentiate the…

Q: An equation of the tangent line to the curve y= cos(x) at a = T/3 is (- 7/3). %3D y =

A:

Q: What is the derivative of y = log b( cos² (ax)) ? Note that a and b are real numbers.

A: we have to find derivative

Q: Find the equation of the tangent line of the function tan (xy²) = 2xy, a J absoleto 700 nu at x = π.

A: Let's find equation of tangent line of given curve at x = pi.

Q: a) What is the slope of the tangent line to the graph of f at x= n ?

A: Given, fx = 4cos2x -2esin3x  We have to to find the slope of the tangent line to the graph of f at x…

Q: 4. Find the equation for the tangent line to the graph of y = VT at a = 2. Remember to keep every…

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of sin ( æ ) = (cos(*") +…

A:

Q: Prove, by Showing all steps i that the 1. derivative of arcos x is 1-メ

A: Derivative of arccosx is -1/√(1-x2)

Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx <2n?…

A: We get the slope y' of the tangent to the function y=tan x-x by differentiating it with respect to…

Q: Find the derivative of t² sin t In Vt +1

A:

Q: I need help evaluating a derivative of a function at the point (pi/2,18pi)

A: We have given

Q: Compute the derivative of h(sin(x)) at æ = 1/6, assuming h'(0.5) 4: %3D

A: As we know that; The Chain Rule: fgx'=f'gx·g'x Let, hfx=hsinx

Q: find an equation of the tangent line at the point indicated.

A: Given equation of curve is  The point on the curve when w=1/8 is given by The slope of the tangent…

Q: The slope of the tangent line to the graph of y = e3 at x = In 2 is

A:

Q: The slope of the tangent line to the graph of y = In(ry) at the point (e, 1) is

A:

Q: To three decimal places, the slope of the tangent to the curve f (x) = log, x , at x = 2 is:

A: First we have to find the differential equation for slope of this function.

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

A:

Q: Determine the equation of the tangent line to g(x) = sin(6x) at x = A.

A: Given ,  g(x) = sin(6x) at x = π  We have to find the equation of the tangent line  g(π) = sin(6π) =…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: