Use formulas (1) and (2) and the power rule to find the derivatives of the following functions. f ( x ) = − 2 x . Derivative of Linear Function If f ( x ) = m x + b , then we have f ' ( x ) = m . ( 1 ) Constant Rule The derivative of a constant function f ( x ) = b is zero. That is, f ' ( x ) = 0 . ( 2 ) Power Rule Let r be any number, and let f ( x ) = x r . Then f ' ( x ) = r x r − 1 .
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions. f ( x ) = − 2 x . Derivative of Linear Function If f ( x ) = m x + b , then we have f ' ( x ) = m . ( 1 ) Constant Rule The derivative of a constant function f ( x ) = b is zero. That is, f ' ( x ) = 0 . ( 2 ) Power Rule Let r be any number, and let f ( x ) = x r . Then f ' ( x ) = r x r − 1 .
Solution Summary: The author explains how to determine the derivative of f(x)=-2x using a linear function.
Find the volume of the solid bounded below by the circular cone z = 2.5√√√x² + y² and above by the
sphere x² + y²+z² = 6.5z.
Electric charge is distributed over the triangular region D shown below so that the charge density at (x, y)
is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m²). Find the total charge on D. Round
your answer to four decimal places.
1
U
5
4
3
2
1
1
2
5
7
coulumbs
Let E be the region bounded cone z = √√/6 - (x² + y²) and the sphere z = x² + y² + z² . Provide an
answer accurate to at least 4 significant digits. Find the volume of E.
Triple Integral
Spherical Coordinates
Cutout of sphere is for visual purposes
0.8-
0.6
z
04
0.2-
0-
-0.4
-0.2
04
0
0.2
0.2
x
-0.2
04 -0.4
Note: The graph is an example. The scale and equation parameters may not be the same for your
particular problem. Round your answer to 4 decimal places.
Hint: Solve the cone equation for phi.
* Oops - try again.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY