Solve 1.5a*15a*15a

$$1.5 a \cdot 15 a \cdot 15 a$$

Evaluate

$$\frac{675a^{3}}{2}$$

Solution Steps

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

$$1.5a^{2}\times 15\times 15a$$

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

$$1.5a^{3}\times 15\times 15$$

Multiply 1.5 and 15 to get 22.5.

$$22.5a^{3}\times 15$$

Multiply 22.5 and 15 to get 337.5.

$$337.5a^{3}$$

Differentiate w.r.t. a

$$\frac{2025a^{2}}{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(1.5a^{2}\times 15\times 15a)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(1.5a^{3}\times 15\times 15)$$

Multiply 1.5 and 15 to get 22.5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(22.5a^{3}\times 15)$$

Multiply 22.5 and 15 to get 337.5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(337.5a^{3})$$

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

$$3\times 337.5a^{3-1}$$

Multiply 3 times 337.5.

$$1012.5a^{3-1}$$

Subtract 1 from 3.

$$1012.5a^{2}$$