Solve 3x^5*7x^9

$$3 x ^ { 5 } \cdot 7 x ^ { 9 }$$

Evaluate

$$21x^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$3x^{14}\times 7$$

Multiply 3 and 7 to get 21.

$$21x^{14}$$

Differentiate w.r.t. x

$$294x^{13}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{14}\times 7)$$

Multiply 3 and 7 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(21x^{14})$$

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

$$14\times 21x^{14-1}$$

Multiply 14 times 21.

$$294x^{14-1}$$

Subtract 1 from 14.

$$294x^{13}$$