Solve frac{64h^{3}k^2l^4}{4h^2kl^-1}

$$\frac { 64 h ^ { 3 } k ^ { 2 } l ^ { 4 } } { 4 h ^ { 2 } k l ^ { - 1 } }$$

Evaluate

$$16hkl^{5}$$

Solution Steps

Cancel out 4kh^{2} in both numerator and denominator.

$$\frac{16hkl^{4}}{\frac{1}{l}}$$

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

$$16hkl^{5}$$

Differentiate w.r.t. h

$$16kl^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{64k^{2}l^{4}l}{4k}h^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}h}(16kl^{5}h^{1})$$

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}.

$$16kl^{5}h^{1-1}$$

Do the arithmetic.

$$16kl^{5}h^{0}$$

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

$$16kl^{5}\times 1$$

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

$$16kl^{5}$$