Solve 6x-3x45/8

$$6x-3x \frac{ 45 }{ 8 }$$

Evaluate

$$-\frac{87x}{8}$$

Solution Steps

Express 3\times \frac{45}{8} as a single fraction.

$$6x-\frac{3\times 45}{8}x$$

Multiply 3 and 45 to get 135.

$$6x-\frac{135}{8}x$$

Combine 6x and -\frac{135}{8}x to get -\frac{87}{8}x.

$$-\frac{87}{8}x$$

Differentiate w.r.t. x

$$-\frac{87}{8} = -10\frac{7}{8} = -10.875$$

Steps Using Definition of a Derivative

Express 3\times \frac{45}{8} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x-\frac{3\times 45}{8}x)$$

Multiply 3 and 45 to get 135.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x-\frac{135}{8}x)$$

Combine 6x and -\frac{135}{8}x to get -\frac{87}{8}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{87}{8}x)$$

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

$$-\frac{87}{8}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{87}{8}x^{0}$$

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

$$-\frac{87}{8}$$