Question

find the derivative (dy/dx) of the given function: 

1. y= e^X sin X

2. y= (cos x)^9

3. 1/ ln(X) 

4. y= ln(1+3x)

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Derivative

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt...

A: A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt...

Q: find the volume of the solid generated by revolving the region about the given line. The region in t...

A: Graph the given situation first: (using graphing calculator) 

Q: In the function:  f(x)= (3x^2)ln(x) , x>0  What are the critical numbers of the function?

A: Given function is

Q: Find, to two decimal places, the x-coordinate of the centroid of the region in the first quadrant bo...

A: Given the x-coordinate of the centroid of the region in the first quadrant bounded by the x-axis, th...

Q: Show that ϕ(t) = e2t is a solution of y′ − 2y = 0 and that y = cϕ(t) is also a solution of this equa...

A: Proof: part (a). Given

Q: Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 14 peo...

A: Let: The number of cartons of food is    x     cartons, x≥0The number of cartons of clothing is   y ...

Q: consider the equation f(x) =5x2 find the average rate of change between x=3 and x=3+x

A: Given: the equation f(x) =5x2 and find the average rate of change between x =3 and x =3+ x

Q: y′=2x/(1+2y),y(2)=0

A: Click to see the answer

Q: The college must build a wheelchair ramp to provide wheelchair access to a building. Federal buildin...

A: We model the equation to suit the criteria given. Question reads that for every 12 inch horizontal d...

Q: You plan to store mercury (w = 849 lb/ft3) in a vertical rectangu-lar tank with a 1 ft square base s...

A: known fact:

Q: Find the equation for the curve in the xy-plane that passes through the point (1, -1) if its slope a...

A: Click to see the answer

Q: Find the centroid of the region cut from the first quadrant by the curve y = 1/sqrt(x + 1) and the l...

A: Click to see the answer

Q: Find the area of the “triangular” region in the first quadrant bounded on the left by the y-axis and...

A: Given: Find the area of the “triangular” region in the first quadrant bounded on the left by the y-a...

Q: (sin t)y′+(cos t)y=et,y(1)=a,0<t<π

A: Given,The initial value problem(sin t)y′+(cos t)y=et, y(1)=a,0<t<πConsider,

Q: See picture below. The question says: "Find the limit or show that it doesn't exist."

A: Given,

Q: Find an equation of the vertical line that passes through (5,6).

A: Generally, the equation of a vertical line that passes through the point (a, b) is x = a .That is , ...

Q: Suppose that you inherit $10,000. The will states how you must invest the money. Some​ (or all) of t...

A: given:

Q: Find the area between the curve y = tan x and the x-axis from x = -pai/4 to x = pai/3.

A: Given information

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the re...

A: Click to see the answer

Q: In a pool filled with water to a depth of 10 ft, calculate the fluid force on one side of a 3 ft by ...

A: a.The integral for Fluid Force Against a Vertical Flat Plate:Suppose that a plate submerged vertical...

Q: Find the volume of the solid generated by revolving the region bounded on the left by the parabola x...

A: (a)Given information:

Q: y′=(3x2−ex)/(2y−5),y(0)

A: Click to see the answer

Q: In the function:  f(x)= (4x^2)/((x^2)+4)  When is the function in concave up and concave down using ...

A: Given:

Q: Suppose that the bacteria in a colony can grow unchecked, by the law of exponential change. The colo...

A:  The colony starts with 1 bacterium and doubles every half-hour.So doubling time of the bacteria = 3...

Q: Consider the function. |r + 7|– |r – 7| f(x) = Estimate the following by evaluating fat x-values nea...

A: Given,

Q: A triangular corner is cut from a square 1 ft on a side. The area of the triangle removed is 36 in2....

A: It is given that the area of triangle is 36 square inches which has been cut from a square.And, a tr...

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the x-coordinates of all local minima and mini...

A: Given:f(x)= (3x^2)ln(x) , x>0

Q: Biologists consider a species of animal or plant to be endangered if it is expected to become extinc...

A: Click to see the answer

Q: Two countries cooperated to airlift​ food, clothing, and other supplies to a blockaded city. The car...

A: Let   x   planes from country A and     y     planes from country B. x≥0, y≥0No more than 44 planes ...

Q: A certain college graduate borrows $8000 to buy a car. The lender charges interest at an annual rate...

A: A certain college graduate borrows $8000 to buy a car. The lender charges interest at an annual rate...

Q: Use the shell method to find the volumes of the solids generated by revolving the regions bounded by...

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: For the function f,Construct and simplify the difference quotient f(x+h)-f(x)/h

A: Given:

Q: Consider the infinite region in the first quadrant bounded by the graphs of y = 1 /x2 , y = 0, and x...

A: Given : The infinite region in the first quadrant bounded by the graphs of y = 1/x2 , y = 0, and x =...

Q: find the volume  The base of the solid is the region in the first quadrant between the line y = x an...

A: Click to see the answer

Q: Find the average value of the function ƒ(x) = 1 /(1 - sin u) on [0, pai/6] .

A: The average value ‘A’ of a function f(x) on any interval (a, b) is given by the formula.

Q: Dreview i. lim h(x) Print Preview j. h (2) k. lim h(x) I. lim h(x) ya 4 6. -4 -2

A: Note:Since you have posted a question with multiple sub-parts, we will solve first four sub-parts fo...

Q: find the volume  The solid lies between planes perpendicular to the x-axis at x = -1 and x = 1. The ...

A: First of all, consider the plot for x = -1, x = 1 and the equation of semicircles on x-y plane.