Solve 49*6a^5/8a^2

$$\frac { 49 \times 6 a ^ { 5 } } { 8 a ^ { 2 } }$$

Evaluate

$$\frac{147a^{3}}{4}$$

Solution Steps

Cancel out 2a^{2} in both numerator and denominator.

$$\frac{3\times 49a^{3}}{4}$$

Multiply 3 and 49 to get 147.

$$\frac{147a^{3}}{4}$$

Differentiate w.r.t. a

$$\frac{441a^{2}}{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{294}{8}a^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{147}{4}a^{3})$$

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}.

$$3\times \frac{147}{4}a^{3-1}$$

Do the arithmetic.

$$\frac{441}{4}a^{2}$$