Solve 5x^5(3x^6)

$$5 x ^ { 5 } ( 3 x ^ { 6 } )$$

Evaluate

$$15x^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$5x^{11}\times 3$$

Multiply 5 and 3 to get 15.

$$15x^{11}$$

Differentiate w.r.t. x

$$165x^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{11}\times 3)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{11})$$

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

$$11\times 15x^{11-1}$$

Multiply 11 times 15.

$$165x^{11-1}$$

Subtract 1 from 11.

$$165x^{10}$$