Solve (-4/7x^7+6x^2-8)^prime

$$( - \frac { 4 } { 7 } x ^ { 7 } + 6 x ^ { 2 } - 8 ) ^ { \prime }$$

Evaluate

$$12x-4x^{6}$$

Steps Using Derivative Rule for Sum

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}.

$$7\left(-\frac{4}{7}\right)x^{7-1}+2\times 6x^{2-1}$$

Multiply 7 times -\frac{4}{7}.

$$-4x^{7-1}+2\times 6x^{2-1}$$

Subtract 1 from 7.

$$-4x^{6}+2\times 6x^{2-1}$$

Multiply 2 times 6.

$$-4x^{6}+12x^{2-1}$$

Subtract 1 from 2.

$$-4x^{6}+12x^{1}$$

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

$$-4x^{6}+12x$$

Differentiate w.r.t. x

$$12-24x^{5}$$