Solve 15w^4div3w

$$15 w ^ { 4 } \div 3 w$$

Evaluate

$$5w^{5}$$

Solution Steps

Divide 15w^{4} by 3 to get 5w^{4}.

$$5w^{4}w$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$5w^{5}$$

Differentiate w.r.t. w

$$25w^{4}$$

Steps Using Definition of a Derivative

Divide 15w^{4} by 3 to get 5w^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w^{4}w)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w^{5})$$

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

$$5\times 5w^{5-1}$$

Multiply 5 times 5.

$$25w^{5-1}$$

Subtract 1 from 5.

$$25w^{4}$$