Solve 2(3-5sqrt{x})-5(x-2sqrt{x})=

$$2 ( 3 - 5 \sqrt { x } ) - 5 ( x - 2 \sqrt { x } ) =$$

Evaluate

$$6-5x$$

Solution Steps

Multiply -1 and 5 to get -5.

$$2\left(3-5\sqrt{x}\right)-5\left(x-2\sqrt{x}\right)$$

Use the distributive property to multiply 2 by 3-5\sqrt{x}.

$$6-10\sqrt{x}-5\left(x-2\sqrt{x}\right)$$

Use the distributive property to multiply -5 by x-2\sqrt{x}.

$$6-10\sqrt{x}-5x+10\sqrt{x}$$

Combine -10\sqrt{x} and 10\sqrt{x} to get 0.

$$6-5x$$

Differentiate w.r.t. x

$$-5$$

Steps Using Derivative Rule for Sum

Multiply -1 and 5 to get -5.

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

Use the distributive property to multiply 2 by 3-5\sqrt{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6-10\sqrt{x}-5\left(x-2\sqrt{x}\right))$$

Use the distributive property to multiply -5 by x-2\sqrt{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6-10\sqrt{x}-5x+10\sqrt{x})$$

Combine -10\sqrt{x} and 10\sqrt{x} to get 0.

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

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}.

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

Subtract 1 from 1.

$$-5x^{0}$$

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

$$-5$$