Solve 12y^7div2y^6=

$$12 y ^ { 7 } \div 2 y ^ { 6 } =$$

Evaluate

$$6y^{13}$$

Solution Steps

Divide 12y^{7} by 2 to get 6y^{7}.

$$6y^{7}y^{6}$$

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$6y^{13}$$

Differentiate w.r.t. y

$$78y^{12}$$

Steps Using Definition of a Derivative

Divide 12y^{7} by 2 to get 6y^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{7}y^{6})$$

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{13})$$

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

$$13\times 6y^{13-1}$$

Multiply 13 times 6.

$$78y^{13-1}$$

Subtract 1 from 13.

$$78y^{12}$$