Solve x^212sqrt{5^2}

$${ x }^{ 2 } 12 \sqrt{ { 5 }^{ 2 } }$$

Evaluate

$$60x^{2}$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$12x^{2}\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$12x^{2}\times 5$$

Multiply 12 and 5 to get 60.

$$60x^{2}$$

Differentiate w.r.t. x

$$120x$$

Steps Using Definition of a Derivative

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}\sqrt{25})$$

Calculate the square root of 25 and get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}\times 5)$$

Multiply 12 and 5 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(60x^{2})$$

The derivative of ax^{n} is nax^{n-1}.

$$2\times 60x^{2-1}$$

Multiply 2 times 60.

$$120x^{2-1}$$

Subtract 1 from 2.

$$120x^{1}$$

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

$$120x$$