Solve 3k^3*5k^3/15k^3

$$\frac { 3 k ^ { 3 } \times 5 k ^ { 3 } } { 15 k ^ { 3 } }$$

Evaluate

$$k^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{3k^{6}\times 5}{15k^{3}}$$

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

$$k^{3}$$

Differentiate w.r.t. k

$$3k^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{15k^{3}}{15}k^{3-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{3}k^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{3})$$

The derivative of a constant term is 0.

$$0$$