Solve 5n^3*4n^4=

$$5 n ^ { 3 } \cdot 4 n ^ { 4 } =$$

Evaluate

$$20n^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$5n^{7}\times 4$$

Multiply 5 and 4 to get 20.

$$20n^{7}$$

Differentiate w.r.t. n

$$140n^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}n}(5n^{7}\times 4)$$

Multiply 5 and 4 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}n}(20n^{7})$$

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

$$7\times 20n^{7-1}$$

Multiply 7 times 20.

$$140n^{7-1}$$

Subtract 1 from 7.

$$140n^{6}$$