Solve -5/8y^4div1/2y^2

$$- \frac { 5 } { 8 } y ^ { 4 } \div \frac { 1 } { 2 } y ^ { 2 }$$

Evaluate

$$-\frac{5y^{6}}{4}$$

Solution Steps

Divide -\frac{5}{8}y^{4} by \frac{1}{2} by multiplying -\frac{5}{8}y^{4} by the reciprocal of \frac{1}{2}.

$$-\frac{5}{8}y^{4}\times 2y^{2}$$

Multiply -\frac{5}{8} and 2 to get -\frac{5}{4}.

$$-\frac{5}{4}y^{4}y^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-\frac{5}{4}y^{6}$$

Differentiate w.r.t. y

$$-\frac{15y^{5}}{2}$$

Steps Using Definition of a Derivative

Divide -\frac{5}{8}y^{4} by \frac{1}{2} by multiplying -\frac{5}{8}y^{4} by the reciprocal of \frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{5}{8}y^{4}\times 2y^{2})$$

Multiply -\frac{5}{8} and 2 to get -\frac{5}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{5}{4}y^{4}y^{2})$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{5}{4}y^{6})$$

The derivative of ax^{n} is nax^{n-1}.

$$6\left(-\frac{5}{4}\right)y^{6-1}$$

Multiply 6 times -\frac{5}{4}.

$$-\frac{15}{2}y^{6-1}$$

Subtract 1 from 6.

$$-\frac{15}{2}y^{5}$$