Solve -3x^2lceil4.4rceil

$$-3 { x }^{ 2 } \lceil 4.4 \rceil$$

Evaluate

$$-15x^{2}$$

Solution Steps

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 4.4 is 5.

$$-3x^{2}\times 5$$

Multiply -3 and 5 to get -15.

$$-15x^{2}$$

Differentiate w.r.t. x

$$-30x$$

Steps Using Definition of a Derivative

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 4.4 is 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{2}\times 5)$$

Multiply -3 and 5 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15x^{2})$$

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

$$2\left(-15\right)x^{2-1}$$

Multiply 2 times -15.

$$-30x^{2-1}$$

Subtract 1 from 2.

$$-30x^{1}$$

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

$$-30x$$