Solve -27/4x^2+10x^2

$$- \frac{ 27 }{ 4 } { x }^{ 2 } +10 { x }^{ 2 }$$

Differentiate w.r.t. x

$$\frac{13x}{2}$$

Steps Using Definition of a Derivative

Combine -\frac{27}{4}x^{2} and 10x^{2} to get \frac{13}{4}x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{13}{4}x^{2})$$

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

$$2\times \frac{13}{4}x^{2-1}$$

Multiply 2 times \frac{13}{4}.

$$\frac{13}{2}x^{2-1}$$

Subtract 1 from 2.

$$\frac{13}{2}x^{1}$$

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

$$\frac{13}{2}x$$

Evaluate

$$\frac{13x^{2}}{4}$$

Solution Steps

Combine -\frac{27}{4}x^{2} and 10x^{2} to get \frac{13}{4}x^{2}.

$$\frac{13}{4}x^{2}$$