Solve (-5k^3-6k+1)+(-6k^2+5k)=

$$( - 5 k ^ { 3 } - 6 k + 1 ) + ( - 6 k ^ { 2 } + 5 k ) =$$

Differentiate w.r.t. k

$$-15k^{2}-12k-1$$

Steps Using Derivative Rule for Sum

Combine -6k and 5k to get -k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(-5k^{3}-k+1-6k^{2})$$

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}.

$$3\left(-5\right)k^{3-1}-k^{1-1}+2\left(-6\right)k^{2-1}$$

Multiply 3 times -5.

$$-15k^{3-1}-k^{1-1}+2\left(-6\right)k^{2-1}$$

Subtract 1 from 3.

$$-15k^{2}-k^{1-1}+2\left(-6\right)k^{2-1}$$

Subtract 1 from 1.

$$-15k^{2}-k^{0}+2\left(-6\right)k^{2-1}$$

Multiply 1 times -1.

$$-15k^{2}-k^{0}-12k^{2-1}$$

Subtract 1 from 2.

$$-15k^{2}-k^{0}-12k^{1}$$

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

$$-15k^{2}-k^{0}-12k$$

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

$$-15k^{2}-1-12k$$

Evaluate

$$1-k-6k^{2}-5k^{3}$$

Solution Steps

Combine -6k and 5k to get -k.

$$-5k^{3}-k+1-6k^{2}$$