Chain Rule

Evaluate The Derivative A

100

If F(x) = f(g(x)), then F'(x) =

F'(x) = f'(g(x)) g'(x)

200

d/dx (sin(2x)) =

cos(2x) · (2)

300

d/dx (tan(x²)) =

sec²(x²) · (2x)

400

d/dx (7-8x)^(1/2) =

(1/2)(7-8x)^(-1/2) · (-8)

500

d/dx -8(4x²+3x)^-4 =

32(4x² +3x)-5 · (8x+3)

Evaluate The Derivative B

100

If G(x) = g(f(x)), then G'(x) =

G'(x) = g'(f(x)) f'(x)

200

d/dx (cos(3x)) =

-sin(3x) · (3)

300

d/dx (sec(2x+3)) =

sec(2x+3)tan(2x+3) · (2)

400

d/dx 7(x+9)^-8 =

-56(x+9)^-9 · (9)

500

d/dx (e^-6t + sin(2-t))³ =

3(e^-6t + sin(2-t))² · (-6e^-6t - cos(2-t))

Evaluate The Derivative C

100

If H(x) = h(k(x)), then H'(x) =

H'(x) = h'(k(x)) k'(x)

200

d/dx (2x+1)^{2 =}

2(2x+1) · (2)

300

d/dx (sin(3x²+4) =

cos(3x²+4) · (6x)

400

d/dx (csc(7x²+5)) =

-csc(7x²+5)cot(7x²+5) · (14x)

500

d/dx (cos(x²e^x) =

-2xe^x + x²e^xsin^{x^2}e^x

Evaluate The Derivative With e

100

If F(x) = e^f(x), then F'(x) =

f'(x)e^f(x)

200

d/dx (e^(7x)) =

7e^7x

300

d/dx (e^1-cos(x)) =

sin(x)e^1-cos(x)

400

d/dx (5+ e^{4x+x^7}) =

(4+7t⁶)e^{4t+t^7}

500

d/dx ((7x^(1/2))+ e^-x) =

(7/2)(7x)^(-1/2) - e^-x