Solve sqrt16^2-175c+4c^2

$$\sqrt { 16 } ^ { 2 } - 175 c + 4 c ^ { 2 }$$

Differentiate w.r.t. c

$$8c-175$$

Steps Using Derivative Rule for Sum

The square of \sqrt{16} is 16.

$$\frac{\mathrm{d}}{\mathrm{d}c}(16-175c+4c^{2})$$

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}.

$$-175c^{1-1}+2\times 4c^{2-1}$$

Subtract 1 from 1.

$$-175c^{0}+2\times 4c^{2-1}$$

Multiply 2 times 4.

$$-175c^{0}+8c^{2-1}$$

Subtract 1 from 2.

$$-175c^{0}+8c^{1}$$

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

$$-175c^{0}+8c$$

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

$$-175+8c$$

Evaluate

$$4c^{2}-175c+16$$

Solution Steps

The square of \sqrt{16} is 16.

$$16-175c+4c^{2}$$