3. Techniques of Differentiation

9–61. Evaluate and simplify y'.

y = e^sin (cosx)

{Use of Tech} Tangent line Find the equation of the line tangent to y=2^sin x at x=π/2. Graph the function and the tangent line.

9–61. Evaluate and simplify y'.

y = 10^sin x+sin¹⁰x

Applying the Chain Rule Use the data in Tables 3.4 and 3.5 of Example 4 to estimate the rate of change in pressure with respect to time experienced by the runner when she is at an altitude of 13,330 ft. Make use of a forward difference quotient when estimating the required derivatives.

Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t² + π.

Find the derivatives of the functions in Exercises 1–42.

𝔂 = 3 .

(5x² + sin 2x)³/²

Find the derivatives of the functions in Exercises 1–42.

𝔂 = (θ² + sec θ + 1)³

Find the derivatives of the functions in Exercises 1–42.

𝔂 = 2 tan² x - sec² x

Find the derivatives of the functions in Exercises 1–42.

s = cos⁴ (1 - 2t)

Find the derivatives of the functions in Exercises 1–42.

s = (sec t + tan t)⁵

Find the derivatives of the functions in Exercises 1–42.

______

𝓻 = √2θ sinθ

Find the derivatives of the functions in Exercises 1–42.

___

𝓻 = sin √ 2θ

Find the derivatives of the functions in Exercises 1–42.

𝔂 = x² sin² (2x²)

Find the derivatives of the functions in Exercises 1–42.

__

𝔂 = ( √ x )²

( 1 + x )

Find the derivatives of the functions in Exercises 1–42.

_____

𝔂 = / x² + x

√ x²