Solve -7{x}^frac{1{3}}-7+2{x}^frac{2{3}}+6

$$-7 { x }^{ \frac{ 1 }{ 3 } } -7+2 { x }^{ \frac{ 2 }{ 3 } } +6$$

Differentiate w.r.t. x

$$\frac{4}{3\sqrt[3]{x}}-\frac{7}{3x^{\frac{2}{3}}}$$

Steps Using Derivative Rule for Sum

Add -7 and 6 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-7x^{\frac{1}{3}}-1+2x^{\frac{2}{3}})$$

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}.

$$\frac{1}{3}\left(-7\right)x^{\frac{1}{3}-1}+\frac{2}{3}\times 2x^{\frac{2}{3}-1}$$

Multiply \frac{1}{3} times -7.

$$-\frac{7}{3}x^{\frac{1}{3}-1}+\frac{2}{3}\times 2x^{\frac{2}{3}-1}$$

Subtract 1 from \frac{1}{3}.

$$-\frac{7}{3}x^{-\frac{2}{3}}+\frac{2}{3}\times 2x^{\frac{2}{3}-1}$$

Multiply \frac{2}{3} times 2.

$$-\frac{7}{3}x^{-\frac{2}{3}}+\frac{4}{3}x^{\frac{2}{3}-1}$$

Subtract 1 from \frac{2}{3}.

$$-\frac{7}{3}x^{-\frac{2}{3}}+\frac{4}{3}x^{-\frac{1}{3}}$$

Evaluate

$$2x^{\frac{2}{3}}-7\sqrt[3]{x}-1$$

Solution Steps

Add -7 and 6 to get -1.

$$-7x^{\frac{1}{3}}-1+2x^{\frac{2}{3}}$$