Solve 12x*50x^2=

$$12x \times 50 { x }^{ 2 } =$$

Evaluate

$$600x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$12x^{3}\times 50$$

Multiply 12 and 50 to get 600.

$$600x^{3}$$

Differentiate w.r.t. x

$$1800x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3}\times 50)$$

Multiply 12 and 50 to get 600.

$$\frac{\mathrm{d}}{\mathrm{d}x}(600x^{3})$$

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

$$3\times 600x^{3-1}$$

Multiply 3 times 600.

$$1800x^{3-1}$$

Subtract 1 from 3.

$$1800x^{2}$$