Im a little confused to a derivative question I have.
y=6x^-6-3^-3
Im confused about y=
Im used to finding the derivative d/dx
Is this the same thing?
My answer is -36/x^7
Sorry if I'm not making sense I'm new to calc.
1. The original equation,
y=6x^-6-3^-3 is just a curve.
2. The
Y here in this specific context means the same as
F(x).
- When you plug in a value for X, and solve the original equation, you get a
Y point as a return value. This is the same thing with linear equations in algebra. That's why it is
Y=
since the equation represents a Y value in the Cartesian plane. Plug in X get a Y back
3. When you "take the derivative" of the original equation,
y=6x^-6-3^-3 ... You are creating a new equation that will be utilized to obtain a
slope of the "tangent line" on any point on the curve. The new equation (derivative) is represented by
F'(x) = Technically y can be used for this too.
- In algebra with a linear equation (line). The slope is the same for every X value you plugin, the slope is always going to be a fixed angle in the XY plane (rise over run).
recall y=mx+b where M is the slope
-With curves such as
y=6x^-6-3^-3 the slope is different at every X point. Each tiny interval along the curve is represented by DX
- When you plug in a value into this new equation
-36/x^7 (which is called the derivative) , you get a
Y point as a return value, but now the
Y return from this new equation represents the
slope at that point (tangent).
-
DY/
DX is the rate of change (or difference) for each tiny slice along the curve. In this context, each time you plugin in a new X into the derivative formula y=
-36/x^7, you a get different Y out. The Y is just a unique slope value.
Conclusion: All the first derivative is doing is allowing you to calculate the slope (Y) for/at every (X). So just think of Y as the slope and DX as the tiny increment between all these slopes.
The whole reason of finding a derivative of a curve is to create a formula that allows you to calculate a slope for every point along the curve.
