Solve 4p/2p*4p^2

$$\frac { 4 p } { 2 p \times 4 p ^ { 2 } }$$

Evaluate

$$\frac{1}{2p^{2}}$$

Solution Steps

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

$$\frac{4p}{2p^{3}\times 4}$$

Cancel out 2\times 2p in both numerator and denominator.

$$\frac{1}{2p^{2}}$$

Differentiate w.r.t. p

$$-\frac{1}{p^{3}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{4}{8p^{2}}p^{1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{1}{2p^{2}}p^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{1}{2p^{2}})$$

The derivative of a constant term is 0.

$$0$$