Solve sqrt[3]{-64/343}quadtext{(k)}sqrt[3]{-0.512}

$$\sqrt[ 3 ] { - \frac { 64 } { 343 } } \quad \text { (k) } \sqrt[ 3 ] { - 0.512 }$$

Evaluate

$$\frac{16k}{35}$$

Solution Steps

Calculate \sqrt[3]{-\frac{64}{343}} and get -\frac{4}{7}.

$$-\frac{4}{7}k\sqrt[3]{-0.512}$$

Calculate \sqrt[3]{-0.512} and get -\frac{4}{5}.

$$-\frac{4}{7}k\left(-\frac{4}{5}\right)$$

Multiply -\frac{4}{7} and -\frac{4}{5} to get \frac{16}{35}.

$$\frac{16}{35}k$$

Differentiate w.r.t. k

$$\frac{16}{35} = 0.45714285714285713$$

Steps Using Definition of a Derivative

Calculate \sqrt[3]{-\frac{64}{343}} and get -\frac{4}{7}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(-\frac{4}{7}k\sqrt[3]{-0.512})$$

Calculate \sqrt[3]{-0.512} and get -\frac{4}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(-\frac{4}{7}k\left(-\frac{4}{5}\right))$$

Multiply -\frac{4}{7} and -\frac{4}{5} to get \frac{16}{35}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{16}{35}k)$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{16}{35}k^{1-1}$$

Subtract 1 from 1.

$$\frac{16}{35}k^{0}$$

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

$$\frac{16}{35}\times 1$$

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

$$\frac{16}{35}$$