Solve d/dxleft(-3left(x-1right)^2+5right)

$$\frac{d}{d x } \left(-3 { \left(x-1 \right) }^{ 2 } +5 \right)$$

Evaluate

$$6-6x$$

Steps Using Derivative Rule for Sum

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3\left(x^{2}-2x+1\right)+5)$$

Use the distributive property to multiply -3 by x^{2}-2x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{2}+6x-3+5)$$

Add -3 and 5 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{2}+6x+2)$$

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}.

$$2\left(-3\right)x^{2-1}+6x^{1-1}$$

Multiply 2 times -3.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$-6x^{1}+6x^{0}$$

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

$$-6x+6x^{0}$$

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

$$-6x+6\times 1$$

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

$$-6x+6$$

Differentiate w.r.t. x

$$-6$$