Solve tan^-1(32.075)a

$$\tan ^ { - 1 } ( 32.075 ) a$$

Evaluate

$$\frac{2500000000000000a}{1566727382625917}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.6266909530503668 ^ {-1} a$$

Calculate 0.6266909530503668 to the power of -1 and get \frac{2500000000000000}{1566727382625917}.

$$\frac{2500000000000000}{1566727382625917}a$$

Differentiate w.r.t. a

$$\frac{2500000000000000}{1566727382625917} = 1\frac{933272617374083}{1566727382625917} = 1.595682840373843$$

Steps Using Definition of a Derivative

Evaluate trigonometric functions in the problem

$$0.6266909530503668 ^ {-1} a$$

Calculate 0.6266909530503668 to the power of -1 and get \frac{2500000000000000}{1566727382625917}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2500000000000000}{1566727382625917}a)$$

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

$$\frac{2500000000000000}{1566727382625917}a^{1-1}$$

Subtract 1 from 1.

$$\frac{2500000000000000}{1566727382625917}a^{0}$$

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

$$\frac{2500000000000000}{1566727382625917}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{2500000000000000}{1566727382625917}$$