Solve 9x^3*2x^4

$$9 x ^ { 3 } \times 2 x ^ { 4 }$$

Evaluate

$$18x^{7}$$

Solution Steps

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

$$9x^{7}\times 2$$

Multiply 9 and 2 to get 18.

$$18x^{7}$$

Differentiate w.r.t. x

$$126x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{7}\times 2)$$

Multiply 9 and 2 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{7})$$

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

$$7\times 18x^{7-1}$$

Multiply 7 times 18.

$$126x^{7-1}$$

Subtract 1 from 7.

$$126x^{6}$$