Solve 4c^2*9c^6=

$$4 c ^ { 2 } \cdot 9 c ^ { 6 } =$$

Evaluate

$$36c^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$4c^{8}\times 9$$

Multiply 4 and 9 to get 36.

$$36c^{8}$$

Differentiate w.r.t. c

$$288c^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}c}(4c^{8}\times 9)$$

Multiply 4 and 9 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}c}(36c^{8})$$

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

$$8\times 36c^{8-1}$$

Multiply 8 times 36.

$$288c^{8-1}$$

Subtract 1 from 8.

$$288c^{7}$$