Solve -5sqrt{6x}*2sqrt{6x}

$$-5 \sqrt{ 6x } \times 2 \sqrt{ 6x }$$

Evaluate

$$-60x$$

Solution Steps

Multiply \sqrt{6x} and \sqrt{6x} to get \left(\sqrt{6x}\right)^{2}.

$$2\left(-5\right)\left(\sqrt{6x}\right)^{2}$$

Multiply 2 and -5 to get -10.

$$-10\left(\sqrt{6x}\right)^{2}$$

Calculate \sqrt{6x} to the power of 2 and get 6x.

$$-10\times 6x$$

Multiply -10 and 6 to get -60.

$$-60x$$

Differentiate w.r.t. x

$$-60$$

Steps Using Definition of a Derivative

Multiply \sqrt{6x} and \sqrt{6x} to get \left(\sqrt{6x}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\left(-5\right)\left(\sqrt{6x}\right)^{2})$$

Multiply 2 and -5 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10\left(\sqrt{6x}\right)^{2})$$

Calculate \sqrt{6x} to the power of 2 and get 6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10\times 6x)$$

Multiply -10 and 6 to get -60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-60x)$$

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

$$-60x^{1-1}$$

Subtract 1 from 1.

$$-60x^{0}$$

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

$$-60$$