Do you have to take the derivative of both sides of an equation?

You can take the derivative of both sides only if both sides are functions. This is not the case. But f(x) is a function, right?

Why can you take the derivative of both sides of an equation?

Differentiating both sides only works if the intersection points of the derivatives happen to fall on the same coordinates (e.g. sinx=cosx, sin′x=cos′x, cosx=sinx, or more trivially if both sides are equal for all variable assignments; that implication doesn’t always work the other way around though: if f(x)≠g(x), then …

Why shouldn’t you ever divide both sides of an equation by a variable or X?

Never divide both sides of the equation by a variable, even if you’re doing it to try to solve a rational equation, because there’s a very real danger that you will actually eliminate answers.

Can I differentiate both sides of an inequality?

Note you can never differentiate with an inequality. Instead, the general idea for checking inequalities with differentiation is that we take h(x)=f(x)−g(x) and then try the derivative test to see whether function is increasing or decreasing.

How do you know when to use implicit differentiation?

When might we want to use implicit differentiation? Implicit differentiation is super useful when you want to find the derivative dy/dx, but x and y are not related in a simple manner like y = ƒ(x).

What does it mean to divide both sides of an equation?

Basically you just multiply the left part (everything before the equals sign) by something, and then do the same to the right side, and put the results together again with an equals sign.

How is solving an equation different to solving an inequality?

The only difference is: If you multiply or divide both sides of an equation by the same negative number, the equation remains the same, but If you multiply or divide both sides of an inequality by the same negative number, the inequality reverses. !!!!!

How do you solve implicit differential equations?

How To Do Implicit Differentiation

1. Take the derivative of every variable.
2. Whenever you take the derivative of “y” you multiply by dy/dx.
3. Solve the resulting equation for dy/dx.

Why is it useful necessary to understand implicit differentiation?

Implicit differentiation is the special case of related rates where one of the variables is time. Implicit differentiation has an important application: it allows to compute the derivatives of inverse functions. It is good that we review this, because we can use these derivatives to find anti-derivatives.