Solve 2x^3*6x^2div4x^4=

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

Evaluate

$$3x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Multiply 2 and 6 to get 12.

$$\frac{12x^{5}}{4}x^{4}$$

Divide 12x^{5} by 4 to get 3x^{5}.

$$3x^{5}x^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$3x^{9}$$

Differentiate w.r.t. x

$$27x^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{5}\times 6}{4}x^{4})$$

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12x^{5}}{4}x^{4})$$

Divide 12x^{5} by 4 to get 3x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{5}x^{4})$$

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{9})$$

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

$$9\times 3x^{9-1}$$

Multiply 9 times 3.

$$27x^{9-1}$$

Subtract 1 from 9.

$$27x^{8}$$