Solve y^-5/y^-6

$$y ^ { - 5 } / y ^ { - 6 }$$

Evaluate

$$y$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -6 from -5 to get 1.

$$y^{1}$$

Calculate y to the power of 1 and get y.

$$y$$

Differentiate w.r.t. y

$$1$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{-5-\left(-6\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{1})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$y^{1-1}$$

Do the arithmetic.

$$y^{0}$$

For any term t except 0, t^{0}=1.

$$1$$