Solve 5b^2[151/b^2]/5b^2[frac{b^3{b}]}

$$\frac { 5 b ^ { 2 } [ \frac { 151 } { b ^ { 2 } } ] } { 5 b ^ { 2 } [ \frac { b ^ { 3 } } { b } ] }$$

Evaluate

$$\frac{151}{b^{4}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$\frac{5b^{2}\times \frac{151}{b^{2}}}{5b^{2}b^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{5b^{2}\times \frac{151}{b^{2}}}{5b^{4}}$$

Express 5\times \frac{151}{b^{2}} as a single fraction.

$$\frac{\frac{5\times 151}{b^{2}}b^{2}}{5b^{4}}$$

Multiply 5 and 151 to get 755.

$$\frac{\frac{755}{b^{2}}b^{2}}{5b^{4}}$$

Cancel out b^{2} and b^{2}.

$$\frac{755}{5b^{4}}$$

Differentiate w.r.t. b

$$-\frac{604}{b^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{5\times \frac{151}{b^{2}}}{5\times \frac{b^{3}}{b}}b^{2-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{151}{b^{4}}b^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{151}{b^{4}})$$

The derivative of a constant term is 0.

$$0$$