How do you solve derivatives?

Answer 1

There are several ways to solve for the derivative:

1. You can use the limit definition: limhà0=(f(x+h)-f(x))/h.
2. You can use the limit at a point definition (when you actually have a point, or if not use #1): limx->a=(f(x)-f(a))/(f-a).
3. Use the short cuts:

• The derivative of a constant like 2 or pi is 0.
• For things raised to a power: d/dx(xn)=nxn-1 where n is any real number.
• Multiplying by a constant, multiply the derivative of u by the constant c: d/dx(cu)=c*du/dx
• Adding, you add the derivative of the first part and the derivative of the second: d/dx(u+v)=du/dx+dv/dx
• Subtracting, you subtract the derivative of the first part and the derivative of the second: d/dx(u-v)=du/dx-dv/dx
• (Multiplying and dividing are more complicated, and you'll just have to memorize their formulas)
• Multiplying, the formula is: d/dx(uv)= u*dv/dx+v*du/dx
• Dividing, the formula is: d/dx(u/v)=(v*du/dx-u*dv/dx)/(v2)
• d/dx(v/u)=(u*dv/dx-v*du/dx)/(u2)