Solve 2x^3y^2*4x^3/y^2

$$\frac { 2 x ^ { 3 } y ^ { 2 } \cdot 4 x ^ { 3 } } { y ^ { 2 } }$$

Evaluate

$$8x^{6}$$

Solution Steps

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

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

Cancel out y^{2} in both numerator and denominator.

$$2\times 4x^{6}$$

Multiply 2 and 4 to get 8.

$$8x^{6}$$

Differentiate w.r.t. x

$$48x^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{6}y^{2}\times 4}{y^{2}})$$

Cancel out y^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\times 4x^{6})$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{6})$$

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

$$6\times 8x^{6-1}$$

Multiply 6 times 8.

$$48x^{6-1}$$

Subtract 1 from 6.

$$48x^{5}$$