Solve y^-4/y^3

$$\frac { y ^ { - 4 } } { y ^ { 3 } }$$

Differentiate w.r.t. y

$$-\frac{7}{y^{8}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{-4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{-7})$$

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}.

$$-7y^{-7-1}$$

Do the arithmetic.

$$-7y^{-8}$$

Evaluate

$$\frac{1}{y^{7}}$$

Solution Steps

Rewrite y^{3} as y^{-4}y^{7}. Cancel out y^{-4} in both numerator and denominator.

$$\frac{1}{y^{7}}$$