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

$$2 x ^ { 2 } \cdot 3 x ^ { 3 } \cdot x ^ { 4 } =$$

Evaluate

$$6x^{9}$$

Solution Steps

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

$$2x^{5}\times 3x^{4}$$

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

$$2x^{9}\times 3$$

Multiply 2 and 3 to get 6.

$$6x^{9}$$

Differentiate w.r.t. x

$$54x^{8}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5}\times 3x^{4})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{9}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{9})$$

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

$$9\times 6x^{9-1}$$

Multiply 9 times 6.

$$54x^{9-1}$$

Subtract 1 from 9.

$$54x^{8}$$