Solve 5x-8x^2-6-5x^2

$$5 x - 8 x ^ { 2 } - 6 - 5 x ^ { 2 }$$

Differentiate w.r.t. x

$$5-26x$$

Steps Using Derivative Rule for Sum

Combine -8x^{2} and -5x^{2} to get -13x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x-13x^{2}-6)$$

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}.

$$5x^{1-1}+2\left(-13\right)x^{2-1}$$

Subtract 1 from 1.

$$5x^{0}+2\left(-13\right)x^{2-1}$$

Multiply 2 times -13.

$$5x^{0}-26x^{2-1}$$

Subtract 1 from 2.

$$5x^{0}-26x^{1}$$

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

$$5x^{0}-26x$$

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

$$5\times 1-26x$$

For any term t, t\times 1=t and 1t=t.

$$5-26x$$

Evaluate

$$-13x^{2}+5x-6$$

Solution Steps

Combine -8x^{2} and -5x^{2} to get -13x^{2}.

$$5x-13x^{2}-6$$