Solve 3x(-3)^2-15x(-3)-95

$$3 x ( - 3 ) ^ { 2 } - 15 x ( - 3 ) - 95$$

Evaluate

$$72x-95$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$3x\times 9-15x\left(-3\right)-95$$

Multiply 3 and 9 to get 27.

$$27x-15x\left(-3\right)-95$$

Multiply 15 and -3 to get -45.

$$27x-\left(-45x\right)-95$$

The opposite of -45x is 45x.

$$27x+45x-95$$

Combine 27x and 45x to get 72x.

$$72x-95$$

Differentiate w.r.t. x

$$72$$

Steps Using Derivative Rule for Sum

Calculate -3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x\times 9-15x\left(-3\right)-95)$$

Multiply 3 and 9 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x-15x\left(-3\right)-95)$$

Multiply 15 and -3 to get -45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x-\left(-45x\right)-95)$$

The opposite of -45x is 45x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x+45x-95)$$

Combine 27x and 45x to get 72x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(72x-95)$$

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}.

$$72x^{1-1}$$

Subtract 1 from 1.

$$72x^{0}$$

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

$$72\times 1$$

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

$$72$$