Solve 5a^4b^-5/2a^-3b^7

$$\frac { 5 a ^ { 4 } b ^ { - 5 } } { 2 a ^ { - 3 } b ^ { 7 } }$$

Evaluate

$$\frac{5a^{7}}{2b^{12}}$$

Solution Steps

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

$$\frac{5b^{-5}a^{7}}{2b^{7}}$$

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

$$\frac{5a^{7}}{2b^{12}}$$

Differentiate w.r.t. a

$$\frac{35a^{6}}{2b^{12}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{b^{5}\times 2b^{7}}a^{4-\left(-3\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{2b^{12}}a^{7})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$7\times \frac{5}{2b^{12}}a^{7-1}$$

Do the arithmetic.

$$\frac{35}{2b^{12}}a^{6}$$