obtain the ava dient to Cu gra equation givey by メ= ln and sigh '2t wh 3.

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

Q: Differentiate y = /sin(x² + 3)cosx

A:

Q: Differentiate the following function.   y = ln(x2 + ex)

A: Given function is y=lnx2+ex. To differentiate the function. Solution: Power rule of differentiation…

Q: Calculate the following derivative: ?/??(ln(tan(2?))+3sin?)

A:

Q: Without using calculator, solve coth−1 x = ln (x + 1).

A:

Q: Use logarithmic function to find dy/dx, if y=(x^2+5)^sin (2x)

A:

Q: dy Use implicit differentiation/logarithm to find dx 4. sin(x+y) = xy + 5

A: We will use implicit differentiation to find the required value.

Q: Differentiate with respect to the independent variable: y=tan[ln(3x2+5)]

A:

Q: Suppose at the end of the d perature stays constant at M furnace/air conditioner rate A

A:

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

Q: Solve by Bernoulli ODE and Integrating Factor: y' = y2+ 3y cotx

A:

Q: What is the velocity (in ft/s) of a sandbag 2.5 s after it is released from a hot-air balloon that…

A: Given that a sandbag is released from a hot-air balloon that is stationary in the air. Then we have…

Q: calculate the derivative. y = sinh(9x)

A: First of all, consider the formula for the chain rule and the given function y. Then assume u and v…

Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

A:

Q: Find dy/dx by implicit differentiation. 5 5 y3 dy/dx = (Express your answer using positive exponents…

A: We have given 5/x^3 + 5/y^3 = 1

Q: a- y= (cosx) (use logarithm differential)

A: To find dy/dx

Q: dy Find using logarithmic differentiation if y = (2z)3z. dz

A: Given, y=2x3x We have to find  dydx using the logarithmic differentiation

Q: (logteペ-1)dx メー

A:

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: find the second derivative and simplify the final result 7. y= Arccos(e^2x)

A: To find     d2arccos(e2x)dx2

Q: Find the given derivative 6 Dx 7x 1 Dx 7x 5 LN +

A:

Q: Find the slope of the tangent line to the exponential function at the point  (0, 1). y = ex/3

A: Slope of tangent line is derivative of the given function at that point.

Q: Differentiate the following function.   y = ln(ex + 3e-x)

A:

Q: Find the derivative of n^(ln⁡(cosu)). Where n=822

A: Given information : nlncosu Here, n=822. we have to find the derivative of given function.

Q: 20. Evaluate the derivative. 4 (sinh ) dx O

A: ddxsinh-1ex

Q: 2. y = [log(arccotx³)]coshx. Find dy/dx

A:

Q: A vertical cylinder is leaking water at a rate of 8m^3/sec. if the cylinder has a height of 10m and…

A: In a vertical cylinder water is leaking at a rate of 8 m3/sec. dVdt=8 Height of the cylinder is 10…

Q: A 25 ft ladder is leaning against a vertical wall. 25 ft At what rate (with respect to time) is the…

A:

Q: write a differential formula that estimates the given change in volume or surface area. The change…

A: write a differential formula that estimates the given change in volume or surface area.

Q: - ton o七

A: Use chain rule of derivative and differentiate one by one in chain form.

Q: write a differential formula that estimates the given change in volume or surface area. The change…

A: To write the differential formula that estimates the given change in volume or surface area.

Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 °,…

A: a. let the hypotenuse of the triangle is h. so using the trigonometric ratio formula,…

Q: How is ln x affected if x is multiplied by et?

A:

Q: 6. y = (x² – 1)tnx

A:

Q: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

A:

Q: Find the derivative of y with respect to s. (56° +3) У3 sec

A:

Q: If ya + Vy = 11 and y(1) = 100, find y'(1) by implicit differentiation.

A: We have to find y'(1).

Q: If an error of 1 percent is made in measuring the edge of a cube, what is the percentage error in…

A: Take the formula of the volume of a cube then differentiate it to get the error in volume.

Q: calculate the derivative y = tanh−1(ln t)

A:

Q: Assign variables and restate the following problem in terms of known and unknown derivatives (but do…

A:

Q: The side of an equilateral triangle increases at the rate of 2 cm/hr. At what rate is the area of…

A: Value=?

Q: In( cosh(3x) - sinh(3x) )=

A:

Q: What is the derivative of : ln cos 3x

A:

Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

A: