Solve 4a^3*6a^5/64a^3

$$\frac { 4 a ^ { 3 } \times 6 a ^ { 5 } } { 64 a ^ { 3 } }$$

Evaluate

$$\frac{3a^{5}}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{4a^{8}\times 6}{64a^{3}}$$

Cancel out 2\times 4a^{3} in both numerator and denominator.

$$\frac{3a^{5}}{8}$$

Differentiate w.r.t. a

$$\frac{15a^{4}}{8}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{24a^{5}}{64}a^{3-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3a^{5}}{8}a^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3a^{5}}{8})$$

The derivative of a constant term is 0.

$$0$$