Solve (-1/7y^6)(5/8y^3)

$$( - \frac { 1 } { 7 } y ^ { 6 } ) ( \frac { 5 } { 8 } y ^ { 3 } )$$

Evaluate

$$-\frac{5y^{9}}{56}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-\frac{1}{7}y^{9}\times \frac{5}{8}$$

Multiply -\frac{1}{7} and \frac{5}{8} to get -\frac{5}{56}.

$$-\frac{5}{56}y^{9}$$

Differentiate w.r.t. y

$$-\frac{45y^{8}}{56}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{1}{7}y^{9}\times \frac{5}{8})$$

Multiply -\frac{1}{7} and \frac{5}{8} to get -\frac{5}{56}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{5}{56}y^{9})$$

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

$$9\left(-\frac{5}{56}\right)y^{9-1}$$

Multiply 9 times -\frac{5}{56}.

$$-\frac{45}{56}y^{9-1}$$

Subtract 1 from 9.

$$-\frac{45}{56}y^{8}$$