Solve 12p^4-4p^3div2p

$$12 p ^ { 4 } - 4 p ^ { 3 } \div 2 p$$

Evaluate

$$10p^{4}$$

Solution Steps

Divide 4p^{3} by 2 to get 2p^{3}.

$$12p^{4}-2p^{3}p$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$12p^{4}-2p^{4}$$

Combine 12p^{4} and -2p^{4} to get 10p^{4}.

$$10p^{4}$$

Differentiate w.r.t. p

$$40p^{3}$$

Steps Using Definition of a Derivative

Divide 4p^{3} by 2 to get 2p^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}p}(12p^{4}-2p^{3}p)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}p}(12p^{4}-2p^{4})$$

Combine 12p^{4} and -2p^{4} to get 10p^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}p}(10p^{4})$$

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

$$4\times 10p^{4-1}$$

Multiply 4 times 10.

$$40p^{4-1}$$

Subtract 1 from 4.

$$40p^{3}$$