Explanation Derivative in mathematics is defined as the rate of change. It is the degree by which the given function is changing at a given point. Derivative is written as d y d x , that means the difference in y divided by the difference in x . Given: A function f ( x , y ) = x + e y and r ( t ) = 〈 3 t – 1 , t 〉 Formula Used: Derivatives of the below functions: 1. Linear Function: d d x ( a x + b ) = a 2. Power Function: d d x ( x a ) = a x a − 1 3. Exponential Function: d d x ( a b f ( x ) ) = a b f ( x ) . f ′ ( x ) . l n ( b ) 4. Logarithmic Function: d d x ( l n ( x ) ) = 1 x 5. Trigonometric Function: a. d d x ( s i n ( x ) ) = c o s ( x ) b. d d x ( c o s ( x ) ) = - s i n ( x ) 6. Sum Rule of Derivative: ( f ( x ) + g ( x ) ) ′ = f ( x ) ′ + g ( x ) ′ 7. Difference Rule of Derivative: ( f ( x ) - g ( x ) ) ′ = f ( x ) ′ - g ( x ) ′ 8. Produce Rule of Derivative: ( f ( x ) g ( x ) ) ′ = f ( x ) ′ g ( x ) + f ( x ) g ( x ) ′ 9...

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

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ISBN: 9781319057664

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14, Problem 29CRE

To determine

The value of $\frac{d}{d t} f (r (t)$ , given that $f (x, y) = x + e^{y}$ and $r (t) = 〈 3 t - 1, t 〉$ at $t = 2$

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Chapter 14, Problem 28CRE

Chapter 14, Problem 30CRE

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Chapter 14 Solutions

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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The value of d d t f ( r ( t ) , given that f ( x , y ) = x + e y and r ( t ) = 〈 3 t – 1 , t 〉 at t = 2

The value of ddt f(r(t), given that f(x, y) = x + ey and r(t) = 〈3t – 1, t〉 at t = 2

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Chapter 14 Solutions

The value of $\frac{d}{d t} f (r (t)$ , given that $f (x, y) = x + e^{y}$ and $r (t) = 〈 3 t - 1, t 〉$ at $t = 2$