Solve 9x*05+2*4x-45x

$$9 x \times 05 + 2 \times 4 x - 45 x$$

Evaluate

$$-37x$$

Solution Steps

Multiply 9 and 0 to get 0.

$$0x\times 5+2\times 4x-45x$$

Multiply 0 and 5 to get 0.

$$0x+2\times 4x-45x$$

Anything times zero gives zero.

$$0+2\times 4x-45x$$

Multiply 2 and 4 to get 8.

$$0+8x-45x$$

Combine 8x and -45x to get -37x.

$$0-37x$$

Anything plus zero gives itself.

$$-37x$$

Differentiate w.r.t. x

$$-37$$

Steps Using Definition of a Derivative

Multiply 9 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0x\times 5+2\times 4x-45x)$$

Multiply 0 and 5 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0x+2\times 4x-45x)$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0+2\times 4x-45x)$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0+8x-45x)$$

Combine 8x and -45x to get -37x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0-37x)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-37x)$$

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

$$-37x^{1-1}$$

Subtract 1 from 1.

$$-37x^{0}$$

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

$$-37$$