Advertisements
Advertisements
Question
Differentiate the following w. r. t. x.: x5 + 3x4
Solution
Let y = x5 + 3x4
Differentiating w.r.t. x, we get
`dy/dx = d/dx (x^5+3x^4)`
= `d/dx x^5 + 3 d/dxx^4`
= 5x4 + 3(4x3)
`dy/dx = 5x^4 + 12x^3`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following functions w. r. t. x.:
`x^(3/2)`
Find the derivative of the following function w. r. t. x.:
`7xsqrt x`
Find the derivative of the following function w. r. t. x.:
35
Differentiate the following w. r. t. x. : `x^(5/2) + 5x^(7/5)`
Differentiate the following w. r. t. x. : `2/7 x^(7/2) + 5/2 x^(2/5)`
Differentiate the following w. r. t. x. : ex log x
Differentiate the following w. r. t. x. : x3 .3x
Find the derivative of the following w. r. t. x by using method of first principle:
sin (3x)
Find the derivative of the following w. r. t. x by using method of first principle:
log (2x + 5)
Find the derivative of the following w. r. t. x by using method of first principle:
tan (2x + 3)
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
`2^(3x + 1)` at x = 2
Discuss the continuity and differentiability of f(x) = x |x| at x = 0
Discuss the continuity and differentiability of f(x) = (2x + 3) |2x + 3| at x = `- 3/2`
Examine the function
f(x) `{:(= x^2 cos (1/x)",", "for" x ≠ 0),(= 0",", "for" x = 0):}`
for continuity and differentiability at x = 0
Determine the values of p and q that make the function f(x) differentiable on R where
f(x) `{:( = "p"x^3",", "for" x < 2),(= x^2 + "q"",", "for" x ≥ 2):}`
Test whether the function f(x) `{:(= 5x - 3x^2",", "for" x ≥ 1),(= 3 - x",", "for" x < 1):}` is differentiable at x = 1
If y = `"e"^x/sqrt(x)` find `("d"y)/("d"x)` when x = 1
