Solve 2x^5*10x^11=

$$2 x ^ { 5 } \cdot 10 x ^ { 11 } =$$

Evaluate

$$20x^{16}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 11 to get 16.

$$2x^{16}\times 10$$

Multiply 2 and 10 to get 20.

$$20x^{16}$$

Differentiate w.r.t. x

$$320x^{15}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 11 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{16}\times 10)$$

Multiply 2 and 10 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20x^{16})$$

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

$$16\times 20x^{16-1}$$

Multiply 16 times 20.

$$320x^{16-1}$$

Subtract 1 from 16.

$$320x^{15}$$