5*2 + 12*3 = 46, not 40. Also, when x = 5 and y = 12, z = +/- 13.b521 said:Homework Statement
If z² = x² + y²
and
dx/dt = 2
and
dy/dt = 3
Find dz/dt when x=5 and y=12
Homework Equations
I used
The Attempt at a Solution
But I resulted in:
2z dz/dt = 2x(dx/dt) + 2y(dy/dt)
Plugged in x,y,dx/dt, and dy/dt to get:
2z (dz/dt) = 2(5)(2) + 2(12)(3)
dz/dt = 80/2z
= 40/z
But the answer is +/- 46/13
b521 said:
A differentiation problem is a mathematical problem that involves finding the rate of change of a function at a specific point. It is used to calculate the slope of a curve at a given point and is an important concept in calculus.
There are two main types of differentiation problems: finding the derivative of a function and finding the equation of a tangent line at a specific point on a curve. Other types include finding the maximum or minimum values of a function, optimization problems, and related rates problems.
The general steps to solve a differentiation problem are: 1) identify the function and the given point; 2) use the basic rules of differentiation to find the derivative of the function; 3) plug in the given point to find the slope at that point; 4) if finding the tangent line, use the point-slope formula to find the equation of the line.
Some common mistakes in differentiation problems include forgetting to use the chain rule, making arithmetic errors, and not simplifying the derivative expression. It is also important to carefully check the units of the final answer to ensure they are consistent with the given units.
To improve your skills in solving differentiation problems, it is important to practice regularly and review the basic rules and formulas. It can also be helpful to work with a study group or seek out extra resources, such as online tutorials or practice problems, to further enhance your understanding of the concepts.
