Solve x^0+3x+10+7x+15-5x+70

$$x ^ { 0 } + 3 x + 10 + 7 x + 15 - 5 x + 70$$

Evaluate

$$5x+96$$

Solution Steps

Calculate x to the power of 0 and get 1.

$$1+3x+10+7x+15-5x+70$$

Add 1 and 10 to get 11.

$$11+3x+7x+15-5x+70$$

Combine 3x and 7x to get 10x.

$$11+10x+15-5x+70$$

Add 11 and 15 to get 26.

$$26+10x-5x+70$$

Combine 10x and -5x to get 5x.

$$26+5x+70$$

Add 26 and 70 to get 96.

$$96+5x$$

Differentiate w.r.t. x

$$5$$

Steps Using Derivative Rule for Sum

Calculate x to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1+3x+10+7x+15-5x+70)$$

Add 1 and 10 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11+3x+7x+15-5x+70)$$

Combine 3x and 7x to get 10x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11+10x+15-5x+70)$$

Add 11 and 15 to get 26.

$$\frac{\mathrm{d}}{\mathrm{d}x}(26+10x-5x+70)$$

Combine 10x and -5x to get 5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(26+5x+70)$$

Add 26 and 70 to get 96.

$$\frac{\mathrm{d}}{\mathrm{d}x}(96+5x)$$

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.

$$5\times 1$$

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

$$5$$