Solve 2x^2*6xdiv3x^4

$$2 x ^ { 2 } \times 6 x \div 3 x ^ { 4 }$$

Evaluate

$$4x^{7}$$

Solution Steps

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

$$\frac{2x^{3}\times 6}{3}x^{4}$$

Multiply 2 and 6 to get 12.

$$\frac{12x^{3}}{3}x^{4}$$

Divide 12x^{3} by 3 to get 4x^{3}.

$$4x^{3}x^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$4x^{7}$$

Differentiate w.r.t. x

$$28x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{3}\times 6}{3}x^{4})$$

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12x^{3}}{3}x^{4})$$

Divide 12x^{3} by 3 to get 4x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}x^{4})$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{7})$$

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

$$7\times 4x^{7-1}$$

Multiply 7 times 4.

$$28x^{7-1}$$

Subtract 1 from 7.

$$28x^{6}$$