Solve sqrt{30^2}+2*sqrt{30}*4x+4x^2

$$\sqrt { 30 ^ { 2 } } + 2 \cdot \sqrt { 30 } \cdot 4 x + 4 x ^ { 2 }$$

Evaluate

$$4x^{2}+8\sqrt{30}x+30$$

Solution Steps

Calculate 30 to the power of 2 and get 900.

$$\sqrt{900}+2\times 4\sqrt{30}x+4x^{2}$$

Calculate the square root of 900 and get 30.

$$30+2\times 4\sqrt{30}x+4x^{2}$$

Multiply 2 and 4 to get 8.

$$30+8\sqrt{30}x+4x^{2}$$

Differentiate w.r.t. x

$$8\left(x+\sqrt{30}\right)$$

Steps Using Derivative Rule for Sum

Calculate 30 to the power of 2 and get 900.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sqrt{900}+2\times 4\sqrt{30}x+4x^{2})$$

Calculate the square root of 900 and get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30+2\times 4\sqrt{30}x+4x^{2})$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30+8\sqrt{30}x+4x^{2})$$

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}.

$$8\sqrt{30}x^{1-1}+2\times 4x^{2-1}$$

Subtract 1 from 1.

$$8\sqrt{30}x^{0}+2\times 4x^{2-1}$$

Multiply 2 times 4.

$$8\sqrt{30}x^{0}+8x^{2-1}$$

Subtract 1 from 2.

$$8\sqrt{30}x^{0}+8x^{1}$$

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

$$8\sqrt{30}x^{0}+8x$$

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

$$8\sqrt{30}\times 1+8x$$

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

$$8\sqrt{30}+8x$$