Solve 1/2*y*(-7)*y^2

$$\frac { 1 } { 2 } \times y \cdot ( - 7 ) \times y ^ { 2 }$$

Evaluate

$$-\frac{7y^{3}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{1}{2}y^{3}\left(-7\right)$$

Multiply \frac{1}{2} and -7 to get -\frac{7}{2}.

$$-\frac{7}{2}y^{3}$$

Differentiate w.r.t. y

$$-\frac{21y^{2}}{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{2}y^{3}\left(-7\right))$$

Multiply \frac{1}{2} and -7 to get -\frac{7}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{7}{2}y^{3})$$

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

$$3\left(-\frac{7}{2}\right)y^{3-1}$$

Multiply 3 times -\frac{7}{2}.

$$-\frac{21}{2}y^{3-1}$$

Subtract 1 from 3.

$$-\frac{21}{2}y^{2}$$