Solve 100%div85*65.8x^2x=

$$100 \% \div 85 \times 65.8 { x }^{ 2 } x=$$

Evaluate

$$\frac{329x^{3}}{425}$$

Solution Steps

Divide 100 by 100 to get 1.

$$\frac{1}{85}\times 65.8x^{2}x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{85}\times 65.8x^{3}$$

Multiply \frac{1}{85} and 65.8 to get \frac{329}{425}.

$$\frac{329}{425}x^{3}$$

Differentiate w.r.t. x

$$\frac{987x^{2}}{425}$$

Steps Using Definition of a Derivative

Divide 100 by 100 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{85}\times 65.8x^{2}x)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{85}\times 65.8x^{3})$$

Multiply \frac{1}{85} and 65.8 to get \frac{329}{425}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{329}{425}x^{3})$$

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

$$3\times \frac{329}{425}x^{3-1}$$

Multiply 3 times \frac{329}{425}.

$$\frac{987}{425}x^{3-1}$$

Subtract 1 from 3.

$$\frac{987}{425}x^{2}$$