Solve 6k^3j^2*5k^3/12k^2

$$\frac { 6 k ^ { 3 } j ^ { 2 } \cdot 5 k ^ { 3 } } { 12 k ^ { 2 } }$$

Evaluate

$$\frac{5j^{2}k^{4}}{2}$$

Solution Steps

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

$$\frac{6k^{6}j^{2}\times 5}{12k^{2}}$$

Cancel out 6k^{2} in both numerator and denominator.

$$\frac{5j^{2}k^{4}}{2}$$

Differentiate w.r.t. k

$$10j^{2}k^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{30j^{2}k^{3}}{12}k^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{5j^{2}k^{3}}{2}k^{1})$$

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}.

$$\frac{5j^{2}k^{3}}{2}k^{1-1}$$

Do the arithmetic.

$$\frac{5j^{2}k^{3}}{2}k^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{5j^{2}k^{3}}{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{5j^{2}k^{3}}{2}$$