Solve (x)^3(-2)^3+sqrt[7]{-8^7}-sqrt[5]{(-1)^5}

$$( x ) ^ { 3 } ( - 2 ) ^ { 3 } + \sqrt[ 7 ] { - 8 ^ { 7 } } - \sqrt[ 5 ] { ( - 1 ) ^ { 5 } }$$

Evaluate

$$-8x^{3}-7$$

Solution Steps

Calculate -2 to the power of 3 and get -8.

$$x^{3}\left(-8\right)+\sqrt[7]{-8^{7}}-\sqrt[5]{\left(-1\right)^{5}}$$

Calculate 8 to the power of 7 and get 2097152.

$$x^{3}\left(-8\right)+\sqrt[7]{-2097152}-\sqrt[5]{\left(-1\right)^{5}}$$

Calculate \sqrt[7]{-2097152} and get -8.

$$x^{3}\left(-8\right)-8-\sqrt[5]{\left(-1\right)^{5}}$$

Calculate -1 to the power of 5 and get -1.

$$x^{3}\left(-8\right)-8-\sqrt[5]{-1}$$

Calculate \sqrt[5]{-1} and get -1.

$$x^{3}\left(-8\right)-8-\left(-1\right)$$

The opposite of -1 is 1.

$$x^{3}\left(-8\right)-8+1$$

Add -8 and 1 to get -7.

$$x^{3}\left(-8\right)-7$$

Differentiate w.r.t. x

$$-24x^{2}$$

Steps Using Derivative Rule for Sum

Calculate -2 to the power of 3 and get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(-8\right)+\sqrt[7]{-8^{7}}-\sqrt[5]{\left(-1\right)^{5}})$$

Calculate 8 to the power of 7 and get 2097152.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(-8\right)+\sqrt[7]{-2097152}-\sqrt[5]{\left(-1\right)^{5}})$$

Calculate \sqrt[7]{-2097152} and get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(-8\right)-8-\sqrt[5]{\left(-1\right)^{5}})$$

Calculate -1 to the power of 5 and get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(-8\right)-8-\sqrt[5]{-1})$$

Calculate \sqrt[5]{-1} and get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(-8\right)-8-\left(-1\right))$$

The opposite of -1 is 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(-8\right)-8+1)$$

Add -8 and 1 to get -7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(-8\right)-7)$$

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}.

$$3\left(-8\right)x^{3-1}$$

Multiply 3 times -8.

$$-24x^{3-1}$$

Subtract 1 from 3.

$$-24x^{2}$$