At , the function passes through the point with a tangent slope of . At , the…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

x = 1

, the function

u = g(x)

passes through the point

(1,4)

with a tangent slope of

0.8

. At

u = 4

, the function

y = f(u)

has a tangent slope of

-2

. Determine

\dfrac{dy}{dx}

x = 1

for the composite function

y = f\bigl(g(x)\bigr)

Related theory

Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability
Differentiation Rules

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