Solve 8b^9(2)^2c^3/4b^3(2)c

$$\frac { 8 b ^ { 9 } ( 2 ) ^ { 2 } c ^ { 3 } } { 4 b ^ { 3 } ( 2 ) c }$$

Evaluate

$$4c^{2}b^{6}$$

Solution Steps

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

$$2^{2}c^{2}b^{6}$$

Calculate 2 to the power of 2 and get 4.

$$4c^{2}b^{6}$$

Differentiate w.r.t. b

$$24c^{2}b^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{32c^{3}}{8c}b^{9-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4c^{2}b^{6})$$

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}.

$$6\times 4c^{2}b^{6-1}$$

Do the arithmetic.

$$24c^{2}b^{5}$$