Solve 2x^2x*25

$$2 { x }^{ 2 } x \times 25$$

Evaluate

$$50x^{3}$$

Solution Steps

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

$$2x^{3}\times 25$$

Multiply 2 and 25 to get 50.

$$50x^{3}$$

Differentiate w.r.t. x

$$150x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}\times 25)$$

Multiply 2 and 25 to get 50.

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

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

$$3\times 50x^{3-1}$$

Multiply 3 times 50.

$$150x^{3-1}$$

Subtract 1 from 3.

$$150x^{2}$$