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

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

Evaluate

$$10-23x$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$4x+6x+5-6^{2}x+3x+5$$

Combine 4x and 6x to get 10x.

$$10x+5-6^{2}x+3x+5$$

Calculate 6 to the power of 2 and get 36.

$$10x+5-36x+3x+5$$

Combine 10x and -36x to get -26x.

$$-26x+5+3x+5$$

Combine -26x and 3x to get -23x.

$$-23x+5+5$$

Add 5 and 5 to get 10.

$$-23x+10$$

Differentiate w.r.t. x

$$-23$$

Steps Using Derivative Rule for Sum

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+6x+5-6^{2}x+3x+5)$$

Combine 4x and 6x to get 10x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x+5-6^{2}x+3x+5)$$

Calculate 6 to the power of 2 and get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x+5-36x+3x+5)$$

Combine 10x and -36x to get -26x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-26x+5+3x+5)$$

Combine -26x and 3x to get -23x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-23x+5+5)$$

Add 5 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-23x+10)$$

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}.

$$-23x^{1-1}$$

Subtract 1 from 1.

$$-23x^{0}$$

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

$$-23$$