Solve 6r*5r^2

$$6 r \cdot 5 r ^ { 2 }$$

Evaluate

$$30r^{3}$$

Solution Steps

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

$$6r^{3}\times 5$$

Multiply 6 and 5 to get 30.

$$30r^{3}$$

Differentiate w.r.t. r

$$90r^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(6r^{3}\times 5)$$

Multiply 6 and 5 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}r}(30r^{3})$$

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

$$3\times 30r^{3-1}$$

Multiply 3 times 30.

$$90r^{3-1}$$

Subtract 1 from 3.

$$90r^{2}$$