Solve -8x/3sqrt[3]{18^30}

$$- \frac { 8 x } { 3 \sqrt[ 3 ] { 18 ^ { 30 } } }$$

Evaluate

$$-\frac{x}{1338925209984}$$

Solution Steps

Calculate 18 to the power of 30 and get 45517159607903340355793714778287898624.

$$-\frac{8x}{3\sqrt[3]{45517159607903340355793714778287898624}}$$

Calculate \sqrt[3]{45517159607903340355793714778287898624} and get 3570467226624.

$$-\frac{8x}{3\times 3570467226624}$$

Multiply 3 and 3570467226624 to get 10711401679872.

$$-\frac{8x}{10711401679872}$$

Divide 8x by 10711401679872 to get \frac{1}{1338925209984}x.

$$-\frac{1}{1338925209984}x$$

Differentiate w.r.t. x

$$-\frac{1}{1338925209984} = -7.468677059355316 \times 10^{-13}$$

Steps Using Definition of a Derivative

Calculate 18 to the power of 30 and get 45517159607903340355793714778287898624.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{8x}{3\sqrt[3]{45517159607903340355793714778287898624}})$$

Calculate \sqrt[3]{45517159607903340355793714778287898624} and get 3570467226624.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{8x}{3\times 3570467226624})$$

Multiply 3 and 3570467226624 to get 10711401679872.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{8x}{10711401679872})$$

Divide 8x by 10711401679872 to get \frac{1}{1338925209984}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{1338925209984}x)$$

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

$$-\frac{1}{1338925209984}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{1}{1338925209984}x^{0}$$

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

$$-\frac{1}{1338925209984}$$