Solve -15x*e^-025x^2

$$-15x \times { e }^{ -025 { x }^{ 2 } }$$

Evaluate

$$-15x$$

Solution Steps

Multiply 0 and 25 to get 0.

$$-15xe^{0x^{2}}$$

Anything times zero gives zero.

$$-15xe^{0}$$

Calculate e to the power of 0 and get 1.

$$-15x$$

Differentiate w.r.t. x

$$-15$$

Steps Using Definition of a Derivative

Multiply 0 and 25 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15xe^{0x^{2}})$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15xe^{0})$$

Calculate e to the power of 0 and get 1.

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

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

$$-15x^{1-1}$$

Subtract 1 from 1.

$$-15x^{0}$$

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

$$-15$$