Solve 4k^5*9k^4/3k^3

$$\frac { 4 k ^ { 5 } \times 9 k ^ { 4 } } { 3 k ^ { 3 } }$$

Evaluate

$$12k^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{4k^{9}\times 9}{3k^{3}}$$

Cancel out 3k^{3} in both numerator and denominator.

$$3\times 4k^{6}$$

Multiply 3 and 4 to get 12.

$$12k^{6}$$

Differentiate w.r.t. k

$$72k^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{36k^{4}}{3}k^{5-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}k}(12k^{4}k^{2})$$

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}.

$$2\times 12k^{4}k^{2-1}$$

Do the arithmetic.

$$24k^{4}k^{1}$$

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

$$24k^{4}k$$