Solve 3c^4*4c^-6*c^-7=

$$3 c ^ { 4 } \times 4 c ^ { - 6 } \times c ^ { - 7 } =$$

Evaluate

$$\frac{12}{c^{9}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -6 to get -2.

$$3c^{-2}\times 4c^{-7}$$

To multiply powers of the same base, add their exponents. Add -2 and -7 to get -9.

$$3c^{-9}\times 4$$

Multiply 3 and 4 to get 12.

$$12c^{-9}$$

Differentiate w.r.t. c

$$-\frac{108}{c^{10}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and -6 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}c}(3c^{-2}\times 4c^{-7})$$

To multiply powers of the same base, add their exponents. Add -2 and -7 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}c}(3c^{-9}\times 4)$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}c}(12c^{-9})$$

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

$$-9\times 12c^{-9-1}$$

Multiply -9 times 12.

$$-108c^{-9-1}$$

Subtract 1 from -9.

$$-108c^{-10}$$