Solve f(x)=3{x^1{-4}}+{x^14}-3x

$$f ( x ) = 3 \{ x ^ { 1 } \{ - 4 \} \} + \{ x ^ { 1 } 4 \} - 3 x$$

Evaluate

$$-11x$$

Solution Steps

Calculate x to the power of 1 and get x.

$$3x\left(-4\right)+x^{1}\times 4-3x$$

Multiply 3 and -4 to get -12.

$$-12x+x^{1}\times 4-3x$$

Calculate x to the power of 1 and get x.

$$-12x+x\times 4-3x$$

Combine -12x and x\times 4 to get -8x.

$$-8x-3x$$

Combine -8x and -3x to get -11x.

$$-11x$$

Differentiate w.r.t. x

$$-11$$

Steps Using Definition of a Derivative

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x\left(-4\right)+x^{1}\times 4-3x)$$

Multiply 3 and -4 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-12x+x^{1}\times 4-3x)$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-12x+x\times 4-3x)$$

Combine -12x and x\times 4 to get -8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8x-3x)$$

Combine -8x and -3x to get -11x.

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

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

$$-11x^{1-1}$$

Subtract 1 from 1.

$$-11x^{0}$$

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

$$-11$$