Solve 2x^20*3x^30

$$2 x ^ { 20 } \cdot 3 x ^ { 30 }$$

Evaluate

$$6x^{50}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 20 and 30 to get 50.

$$2x^{50}\times 3$$

Multiply 2 and 3 to get 6.

$$6x^{50}$$

Differentiate w.r.t. x

$$300x^{49}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 20 and 30 to get 50.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{50}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{50})$$

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

$$50\times 6x^{50-1}$$

Multiply 50 times 6.

$$300x^{50-1}$$

Subtract 1 from 50.

$$300x^{49}$$