You are a piano teacher and must command one of your students to begin playing. How would you do this?
Answer: "Spiel!" Because it's informal, we are going to use the "du" form of the verb "spielen" (to play), which conjugates to "du spielst". Because it's a command form in "du", you're going to need to sweep up the "dust". This means you get rid of the "du" subject and the "st" ending so that "du spielst" becomes "spiel".
If the antiderivative of $$4x^3$$ is $$x^4$$, what is the antiderivative of $$5x^3$$ ?
In this problem we are going to need to use the power rule, which states that when taking the derivative of something with an exponent, you pull down the exponent to in front of the x, then subtract 1 from the exponent. Example: take the derivate of $$x^2$$ we multiply the x by 2 and subtract 1 from the exponent: $$2x^1 = 2x$$ So we do the opposite of that to find the antiderivative. Add one to the exponent and divide the x by the new exponent. So then the answer would be: $$5x^4/4$$
Solve for x: $$ 4x +7 = 3x - 2 $$
$$ x = -9 $$ First, add 2 to both sides: $$ 4x + 9 = 3x $$ Second, subtract $$4x$$ from both sides: $$9=3x-4x $$ --> $$9=-x$$ Lastly, divide both sides by negative one: $$-9 = x$$