Solve 475xxx

$$475xxx$$

Evaluate

$$475x^{3}$$

Solution Steps

Multiply x and x to get x^{2}.

$$475x^{2}x$$

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

$$475x^{3}$$

Differentiate w.r.t. x

$$1425x^{2}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(475x^{2}x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(475x^{3})$$

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

$$3\times 475x^{3-1}$$

Multiply 3 times 475.

$$1425x^{3-1}$$

Subtract 1 from 3.

$$1425x^{2}$$