Solve 3-6n^5-8n^4--6n^4-3n-8n^5

$$3-6 { n }^{ 5 } -8 { n }^{ 4 } --6 { n }^{ 4 } -3n-8 { n }^{ 5 }$$

Evaluate

$$3-3n-2n^{4}-14n^{5}$$

Solution Steps

The opposite of -6n^{4} is 6n^{4}.

$$3-6n^{5}-8n^{4}+6n^{4}-3n-8n^{5}$$

Combine -8n^{4} and 6n^{4} to get -2n^{4}.

$$3-6n^{5}-2n^{4}-3n-8n^{5}$$

Combine -6n^{5} and -8n^{5} to get -14n^{5}.

$$3-14n^{5}-2n^{4}-3n$$

Differentiate w.r.t. n

$$-70n^{4}-8n^{3}-3$$

Steps Using Derivative Rule for Sum

The opposite of -6n^{4} is 6n^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(3-6n^{5}-8n^{4}+6n^{4}-3n-8n^{5})$$

Combine -8n^{4} and 6n^{4} to get -2n^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(3-6n^{5}-2n^{4}-3n-8n^{5})$$

Combine -6n^{5} and -8n^{5} to get -14n^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(3-14n^{5}-2n^{4}-3n)$$

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}.

$$5\left(-14\right)n^{5-1}+4\left(-2\right)n^{4-1}-3n^{1-1}$$

Multiply 5 times -14.

$$-70n^{5-1}+4\left(-2\right)n^{4-1}-3n^{1-1}$$

Subtract 1 from 5.

$$-70n^{4}+4\left(-2\right)n^{4-1}-3n^{1-1}$$

Multiply 4 times -2.

$$-70n^{4}-8n^{4-1}-3n^{1-1}$$

Subtract 1 from 4.

$$-70n^{4}-8n^{3}-3n^{1-1}$$

Subtract 1 from 1.

$$-70n^{4}-8n^{3}-3n^{0}$$

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

$$-70n^{4}-8n^{3}-3$$