Solve 15x^4(3x^9)

$$15 x ^ { 4 } ( 3 x ^ { 9 } )$$

Evaluate

$$45x^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 9 to get 13.

$$15x^{13}\times 3$$

Multiply 15 and 3 to get 45.

$$45x^{13}$$

Differentiate w.r.t. x

$$585x^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 9 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{13}\times 3)$$

Multiply 15 and 3 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(45x^{13})$$

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

$$13\times 45x^{13-1}$$

Multiply 13 times 45.

$$585x^{13-1}$$

Subtract 1 from 13.

$$585x^{12}$$