Solve 3(x-9)*9(757+sqrt{9})

$$3 ( x - 9 ) \times 9 ( 757 + \sqrt { 9 } )$$

Evaluate

$$20520\left(x-9\right)$$

Solution Steps

Multiply 3 and 9 to get 27.

$$27\left(x-9\right)\left(757+\sqrt{9}\right)$$

Calculate the square root of 9 and get 3.

$$27\left(x-9\right)\left(757+3\right)$$

Add 757 and 3 to get 760.

$$27\left(x-9\right)\times 760$$

Multiply 27 and 760 to get 20520.

$$20520\left(x-9\right)$$

Use the distributive property to multiply 20520 by x-9.

$$20520x-184680$$

Differentiate w.r.t. x

$$20520$$

Steps Using Derivative Rule for Sum

Multiply 3 and 9 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27\left(x-9\right)\left(757+\sqrt{9}\right))$$

Calculate the square root of 9 and get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27\left(x-9\right)\left(757+3\right))$$

Add 757 and 3 to get 760.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27\left(x-9\right)\times 760)$$

Multiply 27 and 760 to get 20520.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20520\left(x-9\right))$$

Use the distributive property to multiply 20520 by x-9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20520x-184680)$$

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}.

$$20520x^{1-1}$$

Subtract 1 from 1.

$$20520x^{0}$$

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

$$20520\times 1$$

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

$$20520$$