Solve 8x-1/4x*1/4+0,75x

$$8 x - \frac { 1 } { 4 } x \cdot \frac { 1 } { 4 } + 0,75 x$$

Evaluate

$$\frac{139x}{16}$$

Solution Steps

Multiply \frac{1}{4} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$8x-\frac{1\times 1}{4\times 4}x+0,75x$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 4}.

$$8x-\frac{1}{16}x+0,75x$$

Combine 8x and -\frac{1}{16}x to get \frac{127}{16}x.

$$\frac{127}{16}x+0,75x$$

Combine \frac{127}{16}x and 0,75x to get \frac{139}{16}x.

$$\frac{139}{16}x$$

Differentiate w.r.t. x

$$8,6875$$

Steps Using Definition of a Derivative

Multiply \frac{1}{4} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x-\frac{1\times 1}{4\times 4}x+0,75x)$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x-\frac{1}{16}x+0,75x)$$

Combine 8x and -\frac{1}{16}x to get \frac{127}{16}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{127}{16}x+0,75x)$$

Combine \frac{127}{16}x and 0,75x to get \frac{139}{16}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{139}{16}x)$$

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

$$\frac{139}{16}x^{1-1}$$

Subtract 1 from 1.

$$\frac{139}{16}x^{0}$$

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

$$\frac{139}{16}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{139}{16}$$