Solve 5w*15w*12*25w

$$5 w \cdot 15 w \cdot 12 \cdot 25 w$$

Evaluate

$$22500w^{3}$$

Solution Steps

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

$$5w^{2}\times 15\times 12\times 25w$$

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

$$5w^{3}\times 15\times 12\times 25$$

Multiply 5 and 15 to get 75.

$$75w^{3}\times 12\times 25$$

Multiply 75 and 12 to get 900.

$$900w^{3}\times 25$$

Multiply 900 and 25 to get 22500.

$$22500w^{3}$$

Differentiate w.r.t. w

$$67500w^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w^{2}\times 15\times 12\times 25w)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w^{3}\times 15\times 12\times 25)$$

Multiply 5 and 15 to get 75.

$$\frac{\mathrm{d}}{\mathrm{d}w}(75w^{3}\times 12\times 25)$$

Multiply 75 and 12 to get 900.

$$\frac{\mathrm{d}}{\mathrm{d}w}(900w^{3}\times 25)$$

Multiply 900 and 25 to get 22500.

$$\frac{\mathrm{d}}{\mathrm{d}w}(22500w^{3})$$

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

$$3\times 22500w^{3-1}$$

Multiply 3 times 22500.

$$67500w^{3-1}$$

Subtract 1 from 3.

$$67500w^{2}$$