Solve -7^2+2x(-3)^2-(-6)div(-1/3)^2

$$- 7 ^ { 2 } + 2 x ( - 3 ) ^ { 2 } - ( - 6 ) \div ( - \frac { 1 } { 3 } ) ^ { 2 }$$

Evaluate

$$18x+5$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$-49+2x\left(-3\right)^{2}-\frac{-6}{\left(-\frac{1}{3}\right)^{2}}$$

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

$$-49+2x\times 9-\frac{-6}{\left(-\frac{1}{3}\right)^{2}}$$

Multiply 2 and 9 to get 18.

$$-49+18x-\frac{-6}{\left(-\frac{1}{3}\right)^{2}}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$-49+18x-\frac{-6}{\frac{1}{9}}$$

Divide -6 by \frac{1}{9} by multiplying -6 by the reciprocal of \frac{1}{9}.

$$-49+18x-\left(-6\times 9\right)$$

Multiply -6 and 9 to get -54.

$$-49+18x-\left(-54\right)$$

The opposite of -54 is 54.

$$-49+18x+54$$

Add -49 and 54 to get 5.

$$5+18x$$

Differentiate w.r.t. x

$$18$$

Steps Using Derivative Rule for Sum

Calculate 7 to the power of 2 and get 49.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-49+2x\left(-3\right)^{2}-\frac{-6}{\left(-\frac{1}{3}\right)^{2}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-49+2x\times 9-\frac{-6}{\left(-\frac{1}{3}\right)^{2}})$$

Multiply 2 and 9 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-49+18x-\frac{-6}{\left(-\frac{1}{3}\right)^{2}})$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-49+18x-\frac{-6}{\frac{1}{9}})$$

Divide -6 by \frac{1}{9} by multiplying -6 by the reciprocal of \frac{1}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-49+18x-\left(-6\times 9\right))$$

Multiply -6 and 9 to get -54.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-49+18x-\left(-54\right))$$

The opposite of -54 is 54.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-49+18x+54)$$

Add -49 and 54 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5+18x)$$

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}.

$$18x^{1-1}$$

Subtract 1 from 1.

$$18x^{0}$$

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

$$18\times 1$$

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

$$18$$