Solve frac{10a^{9}b^{8}cd^5}{10a^3b^5cd^3}

$$\frac { 10 a ^ { 9 } b ^ { 8 } c d ^ { 5 } } { 10 a ^ { 3 } b ^ { 5 } c d ^ { 3 } }$$

Differentiate w.r.t. a

$$6d^{2}b^{3}a^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{10cd^{5}b^{8}}{10cd^{3}b^{5}}a^{9-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(d^{2}b^{3}a^{6})$$

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}.

$$6d^{2}b^{3}a^{6-1}$$

Do the arithmetic.

$$6d^{2}b^{3}a^{5}$$

Evaluate

$$d^{2}b^{3}a^{6}$$

Solution Steps

Cancel out 10ca^{3}d^{3}b^{5} in both numerator and denominator.

$$d^{2}b^{3}a^{6}$$