Solve 45a^3b^2div(3a*5b^2)

$$45 a ^ { 3 } b ^ { 2 } \div ( 3 a \times 5 b ^ { 2 } )$$

Differentiate w.r.t. a

$$6a$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{45b^{2}}{15b^{2}}a^{3-1})$$

Do the arithmetic.

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

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}.

$$2\times 3a^{2-1}$$

Do the arithmetic.

$$6a^{1}$$

For any term t, t^{1}=t.

$$6a$$

Evaluate

$$3a^{2}$$

Solution Steps

Cancel out 3\times 5ab^{2} in both numerator and denominator.

$$3a^{2}$$