How to Differentiate Exponentials

Differentiate y = x^3 using the formula y = ax^n: dy/dx = anx^n-1

• 1

  Identify a and n. In the equation y = x^3, a = 1 and n = 3.

• 2

  Subtract 1 from n to comply with the n-1 part of the anx^n-1. In this example, 3-1 is 2, so n-1 is 2.

• 3

  Multiply a by n to comply with the "an" part of the anx^n-1. In this example, 1 x 3 is 3, so "an" is 3.

• 4

  Put the parts of the anx^n-1 derivative together. In our example, "an" is 3 and n-1 is 2, so our final derivative equation is 3x^2. In summary, for y = x^2, dy/dx = 3x^2.

Differentiate y = 4x^5 using the formula y = ax^n: dy/dx = anx^n-1

• 5

  Identify a and n. In the equation y = 4x^5, a = 4 and n = 5.

• 6

  Subtract 1 from n to comply with the n-1 part of the anx^n-1. In this example, 5-1 is 4, so n-1 is 4.

• 7

  Multiply a by n to comply with the "an" part of the anx^n-1. In this example, 4 x 5 is 20, so "an" is 20.

• 8

  Put the parts of the anx^n-1 derivative together. In our example, "an" is 20 and n-1 is 4, so our final derivative equation is 20x^4. In summary, for y = 4x^5, dy/dx = 20x^4.

Diffentiate y = e^6x using the formula y = ae^nx: dy/dx = ane^nx

• 9

  Identify a and n. In the equation y = e^6x , a = 1 and n = 6.

• 10

  Multiply a by n to comply with the "an" part of the ane^nx. In this example, 1 x 6 is 6, so "an" is 6.

• 11

  Put the parts of the ane^nx derivative together. In our example, "an" is 6, so our final derivative equation is 6e^6x. In summary, for y = e^6x, dy/dx = 6e^6x.