Solve 4x^2-7x+x^4+x-15

$$4 x ^ { 2 } - 7 x + x ^ { 4 } + x - 15$$

Differentiate w.r.t. x

$$4x^{3}+8x-6$$

Steps Using Derivative Rule for Sum

Combine -7x and x to get -6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}-6x+x^{4}-15)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 4x^{2-1}-6x^{1-1}+4x^{4-1}$$

Multiply 2 times 4.

$$8x^{2-1}-6x^{1-1}+4x^{4-1}$$

Subtract 1 from 2.

$$8x^{1}-6x^{1-1}+4x^{4-1}$$

Subtract 1 from 1.

$$8x^{1}-6x^{0}+4x^{4-1}$$

Subtract 1 from 4.

$$8x^{1}-6x^{0}+4x^{3}$$

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

$$8x-6x^{0}+4x^{3}$$

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

$$8x-6+4x^{3}$$

Evaluate

$$x^{4}+4x^{2}-6x-15$$

Solution Steps

Combine -7x and x to get -6x.

$$4x^{2}-6x+x^{4}-15$$