Solve |-98/5|x(-32/3)=

$$| - \frac { 98 } { 5 } | x ( - \frac { 32 } { 3 } ) =$$

Evaluate

$$-\frac{3136x}{15}$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{98}{5} is \frac{98}{5}.

$$\frac{98}{5}x\left(-\frac{32}{3}\right)$$

Multiply \frac{98}{5} times -\frac{32}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{98\left(-32\right)}{5\times 3}x$$

Do the multiplications in the fraction \frac{98\left(-32\right)}{5\times 3}.

$$\frac{-3136}{15}x$$

Fraction \frac{-3136}{15} can be rewritten as -\frac{3136}{15} by extracting the negative sign.

$$-\frac{3136}{15}x$$

Differentiate w.r.t. x

$$-\frac{3136}{15} = -209\frac{1}{15} = -209.06666666666666$$

Steps Using Definition of a Derivative

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{98}{5} is \frac{98}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{98}{5}x\left(-\frac{32}{3}\right))$$

Multiply \frac{98}{5} times -\frac{32}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{98\left(-32\right)}{5\times 3}x)$$

Do the multiplications in the fraction \frac{98\left(-32\right)}{5\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3136}{15}x)$$

Fraction \frac{-3136}{15} can be rewritten as -\frac{3136}{15} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{3136}{15}x)$$

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

$$-\frac{3136}{15}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{3136}{15}x^{0}$$

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

$$-\frac{3136}{15}$$