Solve 5x^2*5x*10

$$5 x ^ { 2 } \times 5 x \times 10$$

Evaluate

$$250x^{3}$$

Solution Steps

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

$$5x^{3}\times 5\times 10$$

Multiply 5 and 5 to get 25.

$$25x^{3}\times 10$$

Multiply 25 and 10 to get 250.

$$250x^{3}$$

Differentiate w.r.t. x

$$750x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}\times 5\times 10)$$

Multiply 5 and 5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{3}\times 10)$$

Multiply 25 and 10 to get 250.

$$\frac{\mathrm{d}}{\mathrm{d}x}(250x^{3})$$

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

$$3\times 250x^{3-1}$$

Multiply 3 times 250.

$$750x^{3-1}$$

Subtract 1 from 3.

$$750x^{2}$$