Solve -5x^6-2-7x^6+3x^6-1+7

$$- 5 x ^ { 6 - 2 } - 7 x ^ { 6 } + 3 x ^ { 6 - 1 } + 7$$

Evaluate

$$7-5x^{4}+3x^{5}-7x^{6}$$

Solution Steps

Subtract 2 from 6 to get 4.

$$-5x^{4}-7x^{6}+3x^{6-1}+7$$

Subtract 1 from 6 to get 5.

$$-5x^{4}-7x^{6}+3x^{5}+7$$

Differentiate w.r.t. x

$$\left(-42x^{2}+15x-20\right)x^{3}$$

Steps Using Derivative Rule for Sum

Subtract 2 from 6 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{4}-7x^{6}+3x^{6-1}+7)$$

Subtract 1 from 6 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{4}-7x^{6}+3x^{5}+7)$$

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}.

$$4\left(-5\right)x^{4-1}+6\left(-7\right)x^{6-1}+5\times 3x^{5-1}$$

Multiply 4 times -5.

$$-20x^{4-1}+6\left(-7\right)x^{6-1}+5\times 3x^{5-1}$$

Subtract 1 from 4.

$$-20x^{3}+6\left(-7\right)x^{6-1}+5\times 3x^{5-1}$$

Multiply 6 times -7.

$$-20x^{3}-42x^{6-1}+5\times 3x^{5-1}$$

Subtract 1 from 6.

$$-20x^{3}-42x^{5}+5\times 3x^{5-1}$$

Multiply 6 times -7.

$$-20x^{3}-42x^{5}+15x^{5-1}$$

Subtract 1 from 5.

$$-20x^{3}-42x^{5}+15x^{4}$$