Solve (1/5x^2-y+3/4x)+(-1/5x^2+y-3/2x)+(-frac{11}{8}x^2+frac{3}{4}x)

$$( \frac { 1 } { 5 } x ^ { 2 } - y + \frac { 3 } { 4 } x ) + ( - \frac { 1 } { 5 } x ^ { 2 } + y - \frac { 3 } { 2 } x ) + ( - \frac { 11 } { 8 } x ^ { 2 } + \frac { 3 } { 4 } x )$$

Evaluate

$$-\frac{11x^{2}}{8}$$

Solution Steps

Combine \frac{1}{5}x^{2} and -\frac{1}{5}x^{2} to get 0.

$$-y+\frac{3}{4}x+y-\frac{3}{2}x-\frac{11}{8}x^{2}+\frac{3}{4}x$$

Combine -y and y to get 0.

$$\frac{3}{4}x-\frac{3}{2}x-\frac{11}{8}x^{2}+\frac{3}{4}x$$

Combine \frac{3}{4}x and -\frac{3}{2}x to get -\frac{3}{4}x.

$$-\frac{3}{4}x-\frac{11}{8}x^{2}+\frac{3}{4}x$$

Combine -\frac{3}{4}x and \frac{3}{4}x to get 0.

$$-\frac{11}{8}x^{2}$$

Differentiate w.r.t. x

$$-\frac{11x}{4}$$

Steps Using Definition of a Derivative

Combine \frac{1}{5}x^{2} and -\frac{1}{5}x^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-y+\frac{3}{4}x+y-\frac{3}{2}x-\frac{11}{8}x^{2}+\frac{3}{4}x)$$

Combine -y and y to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4}x-\frac{3}{2}x-\frac{11}{8}x^{2}+\frac{3}{4}x)$$

Combine \frac{3}{4}x and -\frac{3}{2}x to get -\frac{3}{4}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{3}{4}x-\frac{11}{8}x^{2}+\frac{3}{4}x)$$

Combine -\frac{3}{4}x and \frac{3}{4}x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{11}{8}x^{2})$$

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

$$2\left(-\frac{11}{8}\right)x^{2-1}$$

Multiply 2 times -\frac{11}{8}.

$$-\frac{11}{4}x^{2-1}$$

Subtract 1 from 2.

$$-\frac{11}{4}x^{1}$$

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

$$-\frac{11}{4}x$$