Solve 6y^4*y^6/y^2*y^5

$$\frac { 6 y ^ { 4 } \times y ^ { 6 } } { y ^ { 2 } \times y ^ { 5 } }$$

Evaluate

$$6y^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{6y^{10}}{y^{2}y^{5}}$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{6y^{10}}{y^{7}}$$

Cancel out y^{7} in both numerator and denominator.

$$6y^{3}$$

Differentiate w.r.t. y

$$18y^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{6y^{10}}{y^{2}y^{5}})$$

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{6y^{10}}{y^{7}})$$

Cancel out y^{7} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{3})$$

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

$$3\times 6y^{3-1}$$

Multiply 3 times 6.

$$18y^{3-1}$$

Subtract 1 from 3.

$$18y^{2}$$